Details

analyze2.6s (3.8%)

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)

sample58.9s (85%)

Results

54.6s	4111×	body	8192	exit
4.2s	8256×	body	128	valid
43.0ms	84×	body	128	invalid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify47.0ms (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

prune13.0ms (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)

localize50.0ms (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 (.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	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))

series82.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

53.0ms	(.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))))
26.0ms	(.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))

rewrite221.0ms (0.3%)

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:

101.0ms	(.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))))
20.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z))) (/.f64 -3147848041806007/2500000000000 (-.f64 2 z)))
16.0ms	(.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))

simplify373.0ms (0.5%)

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

prune879.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	218	6	224
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	6	226

Error

0.3b

Counts

226 → 6

Alt Table

Status	Error	Program
▶	0.4b	(.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 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))))
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (cbrt.f64 (pow.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))))) (+.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)))) 3)))
	0.4b	(.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 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 (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 4 z) (.f64 (*.f64 (-.f64 2 z) (-.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (-.f64 3 z))))))))))
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (-.f64 (fma.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2)))) (fma.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (fma.f64 2408637854869972117504576098451/7056000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (.f64 395971232097753800969862781701012907/276595200000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))))))))))) (fma.f64 1944029913035397434001281633671/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (fma.f64 1631243975133691160969814893647763/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (+.f64 (.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (sqrt.f64 15/2)) (log.f64 15/2)))) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (sqrt.f64 15/2))))))) (fma.f64 1479421971200822750497987168891/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2)))))) (.f64 1106209385320415913103082059/25200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 3)))))))))))
	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))))))))))
	1.7b	(.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)))) (+.f64 (pow.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))) 3) (pow.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) 3))) (.f64 (pow.f64 (-.f64 15/2 z) z) (fma.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 (+.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 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (-.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (+.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)))))))))

Compiler

Compiled 38195 to 30435 computations (20.3% saved)

localize93.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(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))))
✓	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))))))

series33.0ms (0%)

Counts

4 → 36

Calls

4 calls:

26.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 (PI.f64)))))
4.0ms	(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))))
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))))))
0.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`prod-exp_binary64`
5×	`*-un-lft-identity_binary64`

Counts

4 → 56

Calls

4 calls:

14.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (*.f64 2 (PI.f64)))))
5.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))
0.0ms	(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))))
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))))))

simplify127.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-r_binary64`
377×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
280×	`associate-l_binary64`
279×	`distribute-rgt-in_binary64`

Counts

92 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3667
1	703	3210
2	2530	3079
3	4984	3067
4	5129	3067

prune710.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

0.3b

Counts

117 → 5

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (-.f64 (fma.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2)))) (fma.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (fma.f64 2408637854869972117504576098451/7056000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (.f64 395971232097753800969862781701012907/276595200000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))))))))))) (fma.f64 1944029913035397434001281633671/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (fma.f64 1631243975133691160969814893647763/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (+.f64 (.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (sqrt.f64 15/2)) (log.f64 15/2)))) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (sqrt.f64 15/2))))))) (fma.f64 1479421971200822750497987168891/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2)))))) (.f64 1106209385320415913103082059/25200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 3)))))))))))
	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))))))))))
✓	0.4b	(.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 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))))
▶	0.4b	(.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)) (.f64 (sqrt.f64 2) (sqrt.f64 (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))))
	1.7b	(.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)))) (+.f64 (pow.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))) 3) (pow.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) 3))) (.f64 (pow.f64 (-.f64 15/2 z) z) (fma.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 (+.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 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (-.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (+.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)))))))))

Compiler

Compiled 30449 to 23826 computations (21.8% saved)

localize81.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(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))))
✓	1.0b	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))))
✓	1.0b	(sqrt.f64 (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))))))

series29.0ms (0%)

Counts

2 → 12

Calls

2 calls:

29.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))))
0.0ms	(sqrt.f64 (PI.f64))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`prod-exp_binary64`
16×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
6×	`cbrt-unprod_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 42

Calls

2 calls:

24.0ms	(.f64 (exp.f64 (+.f64 z -15/2)) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))))
1.0ms	(sqrt.f64 (PI.f64))

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-neg_binary64`
823×	`fma-def_binary64`
441×	`associate-r_binary64`
313×	`associate-l_binary64`
258×	`cancel-sign-sub-inv_binary64`

Counts

54 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1855
1	490	1722
2	1960	1613
3	4679	1613
4	5372	1613

prune847.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	128	4	132

Error

0.3b

Counts

132 → 4

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (-.f64 (fma.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2)))) (fma.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (fma.f64 2408637854869972117504576098451/7056000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (.f64 395971232097753800969862781701012907/276595200000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))))))))))) (fma.f64 1944029913035397434001281633671/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (fma.f64 1631243975133691160969814893647763/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (+.f64 (.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (sqrt.f64 15/2)) (log.f64 15/2)))) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (sqrt.f64 15/2))))))) (fma.f64 1479421971200822750497987168891/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2)))))) (.f64 1106209385320415913103082059/25200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 3)))))))))))
✓	0.4b	(.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 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 (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2)))) (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (.f64 (sqrt.f64 2) (sqrt.f64 (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))))
	1.7b	(.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)))) (+.f64 (pow.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))) 3) (pow.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) 3))) (.f64 (pow.f64 (-.f64 15/2 z) z) (fma.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 (+.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 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (-.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (+.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)))))))))

Compiler

Compiled 34100 to 26540 computations (22.2% saved)

localize82.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(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))))
✓	1.0b	(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))
	1.0b	(sqrt.f64 (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))))))

series252.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

252.0ms

(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`cbrt-prod_binary64`
17×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 45

Calls

1 calls:

9.0ms

(*.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2))))

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

628×	`log-div_binary64`
616×	`fma-def_binary64`
388×	`associate-/l*_binary64`
379×	`*-commutative_binary64`
278×	`associate-/r*_binary64`

Counts

57 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	1020
1	153	954
2	404	818
3	1192	711
4	2699	596
5	4184	596
6	5021	596

prune915.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	152	4	156

Error

0.3b

Counts

156 → 4

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (-.f64 (fma.f64 3264229102083425005530891465931403/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/8400000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2)))) (fma.f64 2408637854869972117504576098451/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) (fma.f64 1106209385320415913103082059/4200000000000000000000000 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (fma.f64 2408637854869972117504576098451/7056000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 15/2) 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (.f64 395971232097753800969862781701012907/276595200000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2))))))))))) (fma.f64 1944029913035397434001281633671/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (fma.f64 1631243975133691160969814893647763/2963520000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (pow.f64 z 3) (sqrt.f64 15/2)))))) (+.f64 (.f64 (.f64 1106209385320415913103082059/4200000000000000000000000 (sqrt.f64 (PI.f64))) (+.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z (sqrt.f64 15/2)) (log.f64 15/2)))) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 (log.f64 15/2) (.f64 (.f64 z z) (sqrt.f64 15/2))))))) (fma.f64 1479421971200822750497987168891/3528000000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 (.f64 z z) (sqrt.f64 15/2)))))) (.f64 1106209385320415913103082059/25200000000000000000000000 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 z 3) (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 3)))))))))))
✓	0.4b	(.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 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 (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (cbrt.f64 (exp.f64 (+.f64 z -15/2)))) (.f64 (cbrt.f64 (exp.f64 (+.f64 z -15/2))) (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (.f64 (sqrt.f64 2) (sqrt.f64 (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))))
	1.7b	(.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)))) (+.f64 (pow.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))) 3) (pow.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) 3))) (.f64 (pow.f64 (-.f64 15/2 z) z) (fma.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 (+.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 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (-.f64 (/.f64 3764081837873279/25000000000000000000000 (-.f64 8 z)) (+.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)))))))))

Compiler

Compiled 41062 to 32057 computations (21.9% saved)

regimes1.7s (2.5%)

Accuracy

Total 0.2b remaining (36.9%)

Threshold costs 0.2b (36.9%)

Counts

178 → 1

Compiler

Compiled 56640 to 45668 computations (19.4% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
16×	`+-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	84	388
1	116	388
2	138	388
3	144	388
4	147	388
5	145	388

end914.0ms (1.3%)

Compiler: Compiled 1487 to 1200 computations (19.3% saved)

Details

analyze2.6s (3.8%)

sample58.9s (85%)

simplify47.0ms (0.1%)

prune13.0ms (0%)

localize50.0ms (0.1%)

series82.0ms (0.1%)

rewrite221.0ms (0.3%)

simplify373.0ms (0.5%)

prune879.0ms (1.3%)

localize93.0ms (0.1%)

series33.0ms (0%)

rewrite23.0ms (0%)

simplify127.0ms (0.2%)

prune710.0ms (1%)

localize81.0ms (0.1%)

series29.0ms (0%)

rewrite27.0ms (0%)

simplify83.0ms (0.1%)

prune847.0ms (1.2%)

localize82.0ms (0.1%)

series252.0ms (0.4%)

rewrite11.0ms (0%)

simplify87.0ms (0.1%)

prune915.0ms (1.3%)

regimes1.7s (2.5%)

simplify10.0ms (0%)

end914.0ms (1.3%)

Profiling