Details

analyze2.4s (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)

sample59.6s (80.7%)

Results

55.1s	4087×	body	8192	exit
4.4s	8256×	body	128	valid
54.0ms	92×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify46.0ms (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)

localize49.0ms (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))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series65.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(.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))))
28.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite167.0ms (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:

92.0ms	(.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))))
15.0ms	(+.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))

simplify323.0ms (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

prune1.2s (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	219	5	224
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	221	5	226

Error

0.3b

Counts

226 → 5

Alt Table

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

Compiler

Compiled 38453 to 30647 computations (20.3% saved)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) 7713234287776531/10000000000000)
✓	1.0b	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 (PI.f64)))))
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	2.8b	(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))))))

series35.0ms (0%)

Counts

4 → 36

Calls

4 calls:

30.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 (PI.f64)))))
3.0ms	(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))))))
2.0ms	(.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) 7713234287776531/10000000000000)
0.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`
11×	`associate-*l/_binary64`
10×	`prod-exp_binary64`

Counts

4 → 74

Calls

4 calls:

21.0ms	(.f64 (.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) 7713234287776531/10000000000000)
13.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 (PI.f64)))))
2.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))
0.0ms	(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))))))

simplify111.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

623×	`distribute-rgt-in_binary64`
444×	`associate-r_binary64`
369×	`associate-l_binary64`
274×	`cancel-sign-sub-inv_binary64`
250×	`*-commutative_binary64`

Counts

110 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	305	3181
1	822	2818
2	2968	2697
3	5807	2697

prune1.2s (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

0.3b

Counts

143 → 6

Alt Table

Status	Error	Program
	0.9b	(.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 z -52120709903757078245430659528778613801/100000000000000000000000000000000 -3239171488526100880312595937844772199/50000000000000000000000000000000) (-.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))))
	1.0b	(.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) (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 3 z) (-.f64 4 z)))))) (.f64 (-.f64 8 z) (fma.f64 2496092394504893/250000000000000000000 (.f64 (-.f64 6 z) (.f64 (-.f64 5 z) (.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 3 z) (-.f64 4 z))))) (.f64 (-.f64 7 z) (fma.f64 -3464277381643003/25000000000000000 (.f64 (-.f64 5 z) (.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 3 z) (-.f64 4 z)))) (.f64 (-.f64 6 z) (fma.f64 2501468655737381/200000000000000 (.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 3 z) (-.f64 4 z))) (.f64 (-.f64 5 z) (fma.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) (.f64 (-.f64 3 z) -883075145810703/5000000000000) (.f64 (-.f64 4 z) (fma.f64 (+.f64 (pow.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 3) (pow.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) 3)) (-.f64 3 z) (.f64 (fma.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (-.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))))) 7713234287776531/10000000000000))))))))))))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 (.f64 (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z))) (.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.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 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (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 (pow.f64 (-.f64 15/2 z) 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)) (-.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 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (-.f64 15/2 z)))) (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 (pow.f64 (-.f64 15/2 z) z) (.f64 (-.f64 8 z) (.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))))))))))
	2.2b	(.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 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (.f64 (cbrt.f64 7713234287776531/10000000000000) (cbrt.f64 7713234287776531/10000000000000))) (cbrt.f64 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))))
✓	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))))

Compiler

Compiled 38896 to 30469 computations (21.7% saved)

localize74.0ms (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) 1/2)) (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))

series43.0ms (0.1%)

Counts

3 → 16

Calls

3 calls:

39.0ms

(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (exp.f64 (+.f64 z -15/2)))

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)

rewrite42.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`associate-+l+_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`flip--_binary64`

Counts

3 → 105

Calls

3 calls:

14.0ms

(+.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))

11.0ms

(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (exp.f64 (+.f64 z -15/2)))

3.0ms

(*.f64 9999999999998099/10000000000000000 9999999999998099/10000000000000000)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

566×	`associate-l_binary64`
513×	`associate-r_binary64`
416×	`distribute-rgt-in_binary64`
398×	`fma-def_binary64`
396×	`distribute-lft-in_binary64`

Counts

121 → 191

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	379	5655
1	1261	4697
2	5241	4697

prune1.8s (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	211	5	216

Error

0.3b

Counts

216 → 5

Alt Table

Status	Error	Program
	0.8b	(.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) 1/2)) (exp.f64 (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 -3239171488526100880312595937844772199/50000000000000000000000000000000 (fma.f64 52120709903757078245430659528778613801/100000000000000000000000000000000 z (.f64 6118036922008385701629976080561/6250000000000000000000000 (.f64 z z)))) (-.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 (pow.f64 (-.f64 15/2 z) 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)) (-.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 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (-.f64 15/2 z)))) (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 (pow.f64 (-.f64 15/2 z) z) (.f64 (-.f64 8 z) (.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))))))))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2))) (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (exp.f64 (+.f64 z -15/2))) (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 (pow.f64 (-.f64 15/2 z) 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)) (-.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))))
▶	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) 1/2)) (exp.f64 (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (/.f64 (fma.f64 (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (/.f64 (/.f64 45767980848377092942628957760201/100000000000000000000000000 (-.f64 1 z)) (-.f64 1 z))) (.f64 (-.f64 4 (.f64 z z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (.f64 -3147848041806007/2500000000000 (-.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3))) (+.f64 z 2))) (.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000) (+.f64 z 2))) (-.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 (pow.f64 (-.f64 15/2 z) 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)) (-.f64 8 z)))))

Compiler

Compiled 62600 to 49294 computations (21.3% saved)

localize97.0ms (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 (.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (exp.f64 (+.f64 z -15/2)))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.3b	(fma.f64 (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (/.f64 (/.f64 45767980848377092942628957760201/100000000000000000000000000 (-.f64 1 z)) (-.f64 1 z))) (.f64 (-.f64 4 (.f64 z z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (.f64 -3147848041806007/2500000000000 (-.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3))) (+.f64 z 2)))

series8.0ms (0%)

Counts

2 → 24

Calls

2 calls:

4.0ms

(fma.f64 (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (/.f64 (/.f64 45767980848377092942628957760201/100000000000000000000000000 (-.f64 1 z)) (-.f64 1 z))) (*.f64 (-.f64 4 (*.f64 z z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000)) (*.f64 (*.f64 -3147848041806007/2500000000000 (-.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3))) (+.f64 z 2)))

3.0ms

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

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 59

Calls

2 calls:

27.0ms

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

0.0ms

(fma.f64 (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (/.f64 (/.f64 45767980848377092942628957760201/100000000000000000000000000 (-.f64 1 z)) (-.f64 1 z))) (*.f64 (-.f64 4 (*.f64 z z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000)) (*.f64 (*.f64 -3147848041806007/2500000000000 (-.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3))) (+.f64 z 2)))

simplify117.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-def_binary64`
434×	`fma-neg_binary64`
368×	`associate-l_binary64`
260×	`associate-r_binary64`
246×	`+-commutative_binary64`

Counts

83 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	2866
1	597	2492
2	2227	2439
3	4175	2406
4	4905	2406

prune1.7s (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	181	5	186

Error

0.3b

Counts

186 → 5

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (-.f64 15/2 z)))) (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 (pow.f64 (-.f64 15/2 z) z) (.f64 (-.f64 8 z) (.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))))))))))
	0.5b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (-.f64 15/2 z))) (sqrt.f64 (exp.f64 (+.f64 z -15/2)))) (sqrt.f64 (exp.f64 (+.f64 z -15/2)))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (/.f64 (fma.f64 (-.f64 99999999999961980000000003613801/100000000000000000000000000000000 (/.f64 (/.f64 45767980848377092942628957760201/100000000000000000000000000 (-.f64 1 z)) (-.f64 1 z))) (.f64 (-.f64 4 (.f64 z z)) (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000)) (.f64 (.f64 -3147848041806007/2500000000000 (-.f64 999999999999429700000000108414029999993130164299/1000000000000000000000000000000000000000000000000 (pow.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) 3))) (+.f64 z 2))) (.f64 (fma.f64 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)) (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) 99999999999961980000000003613801/100000000000000000000000000000000) (+.f64 z 2))) (-.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 (pow.f64 (-.f64 15/2 z) 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)) (-.f64 8 z)))))
	0.8b	(.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) 1/2)) (exp.f64 (+.f64 z -15/2))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (-.f64 -3239171488526100880312595937844772199/50000000000000000000000000000000 (fma.f64 52120709903757078245430659528778613801/100000000000000000000000000000000 z (.f64 6118036922008385701629976080561/6250000000000000000000000 (.f64 z z)))) (-.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 (pow.f64 (-.f64 15/2 z) 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)) (-.f64 8 z)))))
	1.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2))) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 (-.f64 15/2 z) 1/2))) (.f64 (.f64 (exp.f64 (+.f64 z -15/2)) (exp.f64 (+.f64 z -15/2))) (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 (pow.f64 (-.f64 15/2 z) 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)) (-.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))))

Compiler

Compiled 57844 to 45523 computations (21.3% saved)

regimes3.4s (4.6%)

Accuracy

Total 0.2b remaining (41%)

Threshold costs 0.2b (41%)

Counts

263 → 1

Compiler

Compiled 111406 to 89950 computations (19.3% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

37×	`*-commutative_binary64`
28×	`+-commutative_binary64`
19×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	462
1	156	462
2	185	462
3	200	462
4	207	462
5	208	462
6	205	462

end1.1s (1.5%)

Compiler: Compiled 2013 to 1614 computations (19.8% saved)

Details

analyze2.4s (3.3%)

sample59.6s (80.7%)

simplify46.0ms (0.1%)

prune12.0ms (0%)

localize49.0ms (0.1%)

series65.0ms (0.1%)

rewrite167.0ms (0.2%)

simplify323.0ms (0.4%)

prune1.2s (1.6%)

localize75.0ms (0.1%)

series35.0ms (0%)

rewrite39.0ms (0.1%)

simplify111.0ms (0.1%)

prune1.2s (1.6%)

localize74.0ms (0.1%)

series43.0ms (0.1%)

rewrite42.0ms (0.1%)

simplify113.0ms (0.2%)

prune1.8s (2.5%)

localize97.0ms (0.1%)

series8.0ms (0%)

rewrite34.0ms (0%)

simplify117.0ms (0.2%)

prune1.7s (2.3%)

regimes3.4s (4.6%)

simplify14.0ms (0%)

end1.1s (1.5%)

Profiling