Details

analyze2.5s (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 127 to 112 computations (11.8% saved)

sample58.1s (76.8%)

Results

53.7s	4040×	body	8192	exit
4.3s	8256×	body	128	valid
61.0ms	119×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+l+_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
224×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	606	119
3	3454	115
4	4863	115
5	4787	115

prune12.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

Status

Error

Program

▶

1.7b

(*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))

1.7b

(*.f64 (/.f64 (PI.f64) (sin.f64 (*.f64 (PI.f64) z))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))

Compiler

Compiled 596 to 508 computations (14.8% saved)

localize53.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))
✓	1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.7b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series73.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

37.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))
29.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
7.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite173.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`frac-add_binary64`
58×	`*-un-lft-identity_binary64`
40×	`distribute-lft-out_binary64`
34×	`associate-*r/_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 126

Calls

4 calls:

96.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z))))
16.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
13.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

simplify309.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
633×	`distribute-rgt-in_binary64`
599×	`distribute-lft-in_binary64`
345×	`*-commutative_binary64`
149×	`associate-l_binary64`

Counts

162 → 224

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	698	20494
1	2393	19568
2	6145	19568

prune922.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	217	7	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	218	8	226

Error

0.2b

Counts

226 → 8

Alt Table

Status	Error	Program
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) 1106209385320415913103082059/4200000000000000000000000 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (*.f64 z (sqrt.f64 15/2)) (log.f64 15/2))))) -1106209385320415913103082059/4200000000000000000000000))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
	2.8b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (exp.f64 (+.f64 (+.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) 2))) (log.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 z -15/2)) (log.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))))) (.f64 (-.f64 7 z) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3) (pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3))))))) (.f64 (.f64 (+.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))) (-.f64 (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))))) (-.f64 7 z)) (-.f64 8 z))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (-.f64 4 z) (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z))) (.f64 (-.f64 5 z) (fma.f64 -883075145810703/5000000000000 (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z)) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 -3147848041806007/2500000000000 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (-.f64 2 z) (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (-.f64 3 z) (.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) 7713234287776531/10000000000000))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))) (.f64 (-.f64 5 z) (fma.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) -883075145810703/5000000000000) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) 7713234287776531/10000000000000) (.f64 (fma.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)))) (-.f64 3 z)))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))

Compiler

Compiled 38601 to 30797 computations (20.2% saved)

localize84.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
✓	1.0b	(*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000)
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.6b	(+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000))

series4.0ms (0%)

Counts

2 → 12

Calls

2 calls:

3.0ms

(+.f64 (*.f64 (-.f64 (*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (*.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (*.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000))

0.0ms

(*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000)

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`associate-+l+_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`flip--_binary64`
20×	`associate-*l/_binary64`

Counts

2 → 83

Calls

2 calls:

11.0ms

(+.f64 (*.f64 (-.f64 (*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (*.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (*.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000))

3.0ms

(*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000)

simplify163.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

416×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
346×	`associate-l_binary64`
324×	`associate-r_binary64`
288×	`fma-def_binary64`

Counts

95 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4537
1	902	3696
2	3804	3591
3	4837	3360
4	4854	3360

prune1.5s (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	217	7	224

Error

0.2b

Counts

224 → 7

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (exp.f64 (+.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (log.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))))) (.f64 (-.f64 7 z) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3) (pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3))))))) (.f64 (.f64 (+.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))) (-.f64 (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))))) (-.f64 7 z)) (-.f64 8 z))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) 1106209385320415913103082059/4200000000000000000000000 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (*.f64 z (sqrt.f64 15/2)) (log.f64 15/2))))) -1106209385320415913103082059/4200000000000000000000000))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))) (.f64 (-.f64 5 z) (fma.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) -883075145810703/5000000000000) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) 7713234287776531/10000000000000) (.f64 (fma.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)))) (-.f64 3 z)))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
▶	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 (exp.f64 (+.f64 z -15/2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))

Compiler

Compiled 63735 to 50341 computations (21% saved)

localize78.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (*.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)
	1.0b	(*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000)
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	2.6b	(+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000))

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 (*.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-*l/_binary64`
28×	`frac-times_binary64`
27×	`flip--_binary64`
27×	`flip3--_binary64`
10×	`add-cbrt-cube_binary64`

Counts

1 → 49

Calls

1 calls:

20.0ms

(*.f64 (*.f64 (*.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)

simplify122.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
352×	`associate-l_binary64`
245×	`associate-r_binary64`
186×	`+-commutative_binary64`
173×	`*-commutative_binary64`

Counts

61 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	1806
1	456	1585
2	1786	1574
3	3014	1549
4	4878	1549
5	4998	1549
6	4928	1549

prune1.7s (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	259	7	266

Error

0.2b

Counts

266 → 7

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (exp.f64 (+.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (log.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
▶	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))))) (.f64 (-.f64 7 z) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3) (pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3))))))) (.f64 (.f64 (+.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))) (-.f64 (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))))) (-.f64 7 z)) (-.f64 8 z))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) 1106209385320415913103082059/4200000000000000000000000 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (*.f64 z (sqrt.f64 15/2)) (log.f64 15/2))))) -1106209385320415913103082059/4200000000000000000000000))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (expm1.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (/.f64 2496092394504893/250000000000000000000 (-.f64 7 z))) (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))) (.f64 (-.f64 5 z) (fma.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) -883075145810703/5000000000000) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) 7713234287776531/10000000000000) (.f64 (fma.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)))) (-.f64 3 z)))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
✓	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 (exp.f64 (+.f64 z -15/2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))

Compiler

Compiled 75296 to 59385 computations (21.1% saved)

localize71.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3)
✓	1.0b	(pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3)
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
	2.7b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series8.0ms (0%)

Counts

3 → 24

Calls

3 calls:

4.0ms

(pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3)

4.0ms

(pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3)

0.0ms

(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite68.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`distribute-lft-out_binary64`
30×	`times-frac_binary64`
29×	`cube-prod_binary64`

Counts

3 → 122

Calls

3 calls:

50.0ms

(pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3)

6.0ms

(pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3)

2.0ms

(sqrt.f64 (*.f64 2 (PI.f64)))

simplify166.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

272×	`distribute-rgt-in_binary64`
246×	`distribute-lft-in_binary64`
216×	`associate-l_binary64`
204×	`fma-def_binary64`
181×	`associate-r_binary64`

Counts

146 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	6010
1	1279	5525
2	4778	5523
3	4958	5523

prune5.7s (7.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	530	1	531
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	531	7	538

Error

0.2b

Counts

538 → 7

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (exp.f64 (+.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (log.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
✓	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))))) (.f64 (-.f64 7 z) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3) (pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3))))))) (.f64 (.f64 (+.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))) (-.f64 (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))))) (-.f64 7 z)) (-.f64 8 z))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) 1106209385320415913103082059/4200000000000000000000000 (fma.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (*.f64 z (sqrt.f64 15/2)) (log.f64 15/2))))) -1106209385320415913103082059/4200000000000000000000000))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2) (+.f64 (-.f64 (-.f64 1 z) 1) 1/2))) (exp.f64 (neg.f64 (+.f64 (+.f64 (-.f64 (-.f64 1 z) 1) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (-.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))))) (.f64 (-.f64 7 z) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) 3) (pow.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) 3))))))) (.f64 (.f64 (+.f64 (.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (+.f64 (+.f64 (+.f64 (/.f64 (fma.f64 -3147848041806007/2500000000000 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (-.f64 2 z) (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z)))) (-.f64 (.f64 (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z)) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))) (*.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (/.f64 7713234287776531/10000000000000 (-.f64 3 z))) (/.f64 -883075145810703/5000000000000 (-.f64 4 z))) (/.f64 2501468655737381/200000000000000 (-.f64 5 z))) (/.f64 -3464277381643003/25000000000000000 (-.f64 6 z))))) (-.f64 7 z)) (-.f64 8 z))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 (PI.f64))))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (-.f64 7 z) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) (-.f64 4 z))) (.f64 (-.f64 5 z) (fma.f64 (.f64 (-.f64 2 z) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (-.f64 3 z) -883075145810703/5000000000000) (.f64 (-.f64 4 z) (fma.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) 7713234287776531/10000000000000) (.f64 (fma.f64 -3147848041806007/2500000000000 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) -9999999999998099/10000000000000000) 99999999999961980000000003613801/100000000000000000000000000000000) (.f64 (-.f64 2 z) (+.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3)))) (-.f64 3 z)))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (-.f64 (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))
✓	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 (exp.f64 (+.f64 z -15/2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000) (.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 2 z)) (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) -3147848041806007/2500000000000)) (-.f64 3 z)) (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) 7713234287776531/10000000000000)) (-.f64 4 z)) (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) -883075145810703/5000000000000)) (-.f64 5 z)) (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) 2501468655737381/200000000000000)) (-.f64 6 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) -3464277381643003/25000000000000000)) (-.f64 7 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) 2496092394504893/250000000000000000000)) (-.f64 8 z)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) 3764081837873279/25000000000000000000000))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (-.f64 2 z)) (-.f64 3 z)) (-.f64 4 z)) (-.f64 5 z)) (-.f64 6 z)) (-.f64 7 z)) (-.f64 8 z))))

Compiler

Compiled 229679 to 189537 computations (17.5% saved)

regimes2.6s (3.4%)

Accuracy

Total 0.2b remaining (40%)

Threshold costs 0.2b (40%)

Counts

163 → 1

Compiler

Compiled 84554 to 69456 computations (17.9% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
23×	`+-commutative_binary64`
15×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	388
1	134	388
2	156	388
3	162	388
4	165	388
5	162	388

end1.2s (1.5%)

Compiler: Compiled 2382 to 1954 computations (18% saved)

Details

analyze2.5s (3.3%)

sample58.1s (76.8%)

simplify48.0ms (0.1%)

prune12.0ms (0%)

localize53.0ms (0.1%)

series73.0ms (0.1%)

rewrite173.0ms (0.2%)

simplify309.0ms (0.4%)

prune922.0ms (1.2%)

localize84.0ms (0.1%)

series4.0ms (0%)

rewrite28.0ms (0%)

simplify163.0ms (0.2%)

prune1.5s (2%)

localize78.0ms (0.1%)

series3.0ms (0%)

rewrite28.0ms (0%)

simplify122.0ms (0.2%)

prune1.7s (2.2%)

localize71.0ms (0.1%)

series8.0ms (0%)

rewrite68.0ms (0.1%)

simplify166.0ms (0.2%)

prune5.7s (7.5%)

regimes2.6s (3.4%)

simplify11.0ms (0%)

end1.2s (1.5%)

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