Details

analyze2.3s (3.2%)

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)

sample58.4s (81.7%)

Results

54.0s	3999×	body	8192	exit
4.3s	8256×	body	128	valid
47.0ms	87×	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

prune11.0ms (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

1.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.9b	(.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)))))
▶	1.9b	(.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

1.9b

(*.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)))))

▶

1.9b

(*.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)

localize51.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	1.2b	(.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))))
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
✓	4.8b	(-.f64 (-.f64 1 z) 1)

series32.0ms (0%)

Counts

4 → 36

Calls

4 calls:

28.0ms	(.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))))
2.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
1.0ms	(-.f64 (-.f64 1 z) 1)
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite79.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

582×	`log1p-udef_binary64`
326×	`log1p-expm1-u_binary64`
326×	`expm1-log1p-u_binary64`
317×	`add-log-exp_binary64`
315×	`add-exp-log_binary64`

Counts

4 → 82

Calls

4 calls:

77.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))
77.0ms	(.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))))
77.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
77.0ms	(-.f64 (-.f64 1 z) 1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	83
1	684	66
2	4938	66
3	5704	66

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
599×	`*-commutative_binary64`
365×	`associate-+l+_binary64`
323×	`sub-neg_binary64`
270×	`associate-r_binary64`

Counts

118 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1007
1	397	1005
2	1402	893
3	4603	893
4	5005	893

prune931.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	330	6	336
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	332	6	338

Error

0.5b

Counts

338 → 6

Alt Table

Status	Error	Program
	1.9b	(.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 (log.f64 (/.f64 1 (exp.f64 z))) 7) 1/2)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.9b	(.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 2))) (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.9b	(.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 (fma.f64 (sqrt.f64 (-.f64 1 z)) (sqrt.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 14/15 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))))) (+.f64 (.f64 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (+.f64 (.f64 (.f64 (exp.f64 -15/2) (pow.f64 (log.f64 15/2) 2)) (.f64 (sqrt.f64 (PI.f64)) 7/15)) (.f64 892/3375 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2))))) (-.f64 (.f64 (.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)))))) -127/225) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (log.f64 15/2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 14/15 (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (.f64 1/6 (.f64 (sqrt.f64 2) (.f64 (*.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (pow.f64 (log.f64 15/2) 3)))))))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.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 (fma.f64 z 904338909853211/2500000000000 479507597606835099/10000000000000000) (/.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 43538 to 36648 computations (15.8% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2))))
✓	2.2b	(pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3)
	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
	4.8b	(-.f64 (-.f64 1 z) 1)

series1.2s (1.6%)

Counts

2 → 24

Calls

2 calls:

1.1s

(pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3)

29.0ms

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

rewrite72.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

311×	`log1p-udef_binary64`
199×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`

Counts

2 → 55

Calls

2 calls:

71.0ms

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

71.0ms

(pow.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	70
1	429	54
2	4432	54
3	4853	54

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

579×	`sub-neg_binary64`
568×	`associate-+l+_binary64`
487×	`cancel-sign-sub-inv_binary64`
411×	`associate--l+_binary64`
329×	`associate-r_binary64`

Counts

79 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1627
1	441	1595
2	1643	1356
3	4624	1356
4	5229	1356

prune818.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	277	3	280
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	280	6	286

Error

0.5b

Counts

286 → 6

Alt Table

Status	Error	Program
	1.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (-.f64 (+.f64 (.f64 (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (sqrt.f64 (PI.f64))) (.f64 14/15 (.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))))) (.f64 (.f64 (exp.f64 -15/2) (.f64 (log.f64 15/2) (.f64 (sqrt.f64 2) (.f64 z (sqrt.f64 15/2))))) (sqrt.f64 (PI.f64)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.9b	(.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 2))) (sqrt.f64 (PI.f64))) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 14/15 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))))) (+.f64 (.f64 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (+.f64 (.f64 (.f64 (exp.f64 -15/2) (pow.f64 (log.f64 15/2) 2)) (.f64 (sqrt.f64 (PI.f64)) 7/15)) (.f64 892/3375 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2))))) (-.f64 (.f64 (.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)))))) -127/225) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (log.f64 15/2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 14/15 (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (.f64 1/6 (.f64 (sqrt.f64 2) (.f64 (*.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (pow.f64 (log.f64 15/2) 3)))))))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.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 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (+.f64 (neg.f64 z) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.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 (fma.f64 z 904338909853211/2500000000000 479507597606835099/10000000000000000) (/.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 34529 to 28054 computations (18.8% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.2b	(pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3)
	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
✓	4.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1)
	4.8b	(-.f64 (-.f64 1 z) 1)

series113.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

113.0ms

(fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1)

rewrite71.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
135×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`
132×	`prod-diff_binary64`

Counts

1 → 25

Calls

1 calls:

71.0ms

(fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7
1	178	7
2	1790	7
3	4955	7
4	4884	7

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

706×	`log-prod_binary64`
416×	`associate-l_binary64`
394×	`associate-r_binary64`
302×	`div-sub_binary64`
268×	`fma-def_binary64`

Counts

37 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	72
1	55	68
2	115	66
3	276	38
4	841	38
5	3841	38
6	4847	38
7	4376	38
8	4567	38

prune900.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	278	6	284

Error

0.5b

Counts

284 → 6

Alt Table

Status	Error	Program
	1.9b	(.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 2))) (sqrt.f64 (PI.f64))) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 14/15 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))))) (+.f64 (.f64 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (+.f64 (.f64 (.f64 (exp.f64 -15/2) (pow.f64 (log.f64 15/2) 2)) (.f64 (sqrt.f64 (PI.f64)) 7/15)) (.f64 892/3375 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2))))) (-.f64 (.f64 (.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)))))) -127/225) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (log.f64 15/2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 14/15 (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (.f64 1/6 (.f64 (sqrt.f64 2) (.f64 (*.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (pow.f64 (log.f64 15/2) 3)))))))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.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 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (+.f64 (neg.f64 z) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.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 (fma.f64 z 904338909853211/2500000000000 479507597606835099/10000000000000000) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
▶	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (log.f64 (/.f64 1 (exp.f64 z))) 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 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.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 35557 to 28954 computations (18.6% saved)

localize63.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (log.f64 (/.f64 1 (exp.f64 z))) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
	4.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1)
✓	4.8b	(log.f64 (/.f64 1 (exp.f64 z)))
	4.8b	(-.f64 (-.f64 1 z) 1)

series171.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

166.0ms

(log.f64 (/.f64 1 (exp.f64 z)))

5.0ms

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

rewrite78.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

358×	`prod-diff_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
195×	`add-sqr-sqrt_binary64`
189×	`add-log-exp_binary64`

Counts

2 → 92

Calls

2 calls:

76.0ms

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

76.0ms

(log.f64 (/.f64 1 (exp.f64 z)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	417	20
2	4303	20
3	4900	20

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
542×	`associate-l_binary64`
542×	`unswap-sqr_binary64`
311×	`associate-r_binary64`
262×	`associate-/r*_binary64`

Counts

108 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	273
1	117	223
2	263	220
3	599	213
4	1151	210
5	3267	210
6	4884	210
7	4997	210

prune1.8s (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	276	6	282

Error

0.5b

Counts

282 → 6

Alt Table

Status	Error	Program
	1.9b	(.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 2))) (sqrt.f64 (PI.f64))) (+.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)))))
	2.1b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 15/2)) (.f64 14/15 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 127/225 (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2)))) (.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 z (.f64 z (sqrt.f64 15/2))) (pow.f64 (log.f64 15/2) 2))))))) (+.f64 (.f64 (.f64 (pow.f64 z 3) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (+.f64 (.f64 (.f64 (exp.f64 -15/2) (pow.f64 (log.f64 15/2) 2)) (.f64 (sqrt.f64 (PI.f64)) 7/15)) (.f64 892/3375 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2))))) (-.f64 (.f64 (.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)))))) -127/225) (fma.f64 (sqrt.f64 (PI.f64)) (.f64 (exp.f64 -15/2) (.f64 (.f64 z (.f64 (sqrt.f64 2) (sqrt.f64 15/2))) (log.f64 15/2))) (.f64 (.f64 (sqrt.f64 (PI.f64)) (exp.f64 -15/2)) (+.f64 (.f64 14/15 (.f64 (log.f64 15/2) (.f64 (.f64 z z) (.f64 (sqrt.f64 2) (sqrt.f64 15/2))))) (.f64 1/6 (.f64 (sqrt.f64 2) (.f64 (*.f64 (pow.f64 z 3) (sqrt.f64 15/2)) (pow.f64 (log.f64 15/2) 3)))))))))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.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 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.f64 (-.f64 1 z)) -1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (sqrt.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (-.f64 1 z)))) (/.f64 -3147848041806007/2500000000000 (+.f64 (neg.f64 z) 2))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
	1.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.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 (fma.f64 z 904338909853211/2500000000000 479507597606835099/10000000000000000) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8)))))
✓	0.7b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (neg.f64 z) 15/2) (+.f64 (neg.f64 z) 1/2))) (exp.f64 (neg.f64 (+.f64 (neg.f64 z) 15/2)))) 3) 1/3) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (log.f64 (/.f64 1 (exp.f64 z))) 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 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 z)) 2) (cbrt.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 34921 to 28184 computations (19.3% saved)

regimes3.4s (4.8%)

Accuracy

Total 0.2b remaining (40.8%)

Threshold costs 0.2b (40.8%)

Counts

435 → 1

Compiler

Compiled 103206 to 88404 computations (14.3% saved)

simplify31.0ms (0%)

Algorithm

1×	egg-herbie

Rules

123×	`cancel-sign-sub-inv_binary64`
89×	`distribute-rgt-neg-in_binary64`
60×	`distribute-neg-in_binary64`
57×	`distribute-lft-neg-in_binary64`
57×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	4294967295
1	107	4294967295
2	121	4294967295
3	131	4294967295
4	137	4294967295
5	149	4294967295
6	157	4294967295
7	170	4294967295
8	185	4294967295
9	203	4294967295
10	231	4294967295
11	259	4294967295
12	289	4294967295
13	329	4294967295
14	371	4294967295
15	413	4294967295
16	455	4294967295
17	497	4294967295
18	540	4294967295
19	575	4294967295
20	594	4294967295
21	603	4294967295
22	605	4294967295
23	580	4294967295

end527.0ms (0.7%)

Compiler: Compiled 1056 to 912 computations (13.6% saved)

Details

analyze2.3s (3.2%)

sample58.4s (81.7%)

simplify47.0ms (0.1%)

prune11.0ms (0%)

localize51.0ms (0.1%)

series32.0ms (0%)

rewrite79.0ms (0.1%)

simplify62.0ms (0.1%)

prune931.0ms (1.3%)

localize61.0ms (0.1%)

series1.2s (1.6%)

rewrite72.0ms (0.1%)

simplify77.0ms (0.1%)

prune818.0ms (1.1%)

localize62.0ms (0.1%)

series113.0ms (0.2%)

rewrite71.0ms (0.1%)

simplify99.0ms (0.1%)

prune900.0ms (1.3%)

localize63.0ms (0.1%)

series171.0ms (0.2%)

rewrite78.0ms (0.1%)

simplify66.0ms (0.1%)

prune1.8s (2.5%)

regimes3.4s (4.8%)

simplify31.0ms (0%)

end527.0ms (0.7%)

Profiling