Details

analyze4.7s (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%	25.1%	25.1%	11
49.9%	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)

sample1.5min (59.4%)

Results

1.4min	3870×	body	8192	exit
6.9s	8256×	body	128	valid

Compiler

Compiled 378 to 334 computations (11.6% saved)

simplify77.0ms (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

prune25.0ms (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

2.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.9b	(.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)))))
▶	2.9b	(.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

2.9b

(*.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)))))

▶

2.9b

(*.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)

localize105.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	1.9b	(.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))))
✓	2.7b	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
✓	4.5b	(-.f64 (-.f64 1 z) 1)

series71.0ms (0%)

Counts

4 → 36

Calls

4 calls:

63.0ms	(.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))))
5.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
3.0ms	(-.f64 (-.f64 1 z) 1)
0.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

rewrite161.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
27×	`prod-diff_binary64`
24×	`add-cube-cbrt_binary64`
14×	`add-log-exp_binary64`

Counts

4 → 125

Calls

4 calls:

68.0ms	(.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))))
59.0ms	(+.f64 (+.f64 9999999999998099/10000000000000000 (/.f64 6765203681218851/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 1))) (/.f64 -3147848041806007/2500000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 2)))
15.0ms	(-.f64 (-.f64 1 z) 1)
3.0ms	(sqrt.f64 (*.f64 (PI.f64) 2))

simplify187.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

397×	`associate-r_binary64`
385×	`fma-neg_binary64`
333×	`associate-l_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`times-frac_binary64`

Counts

161 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	3671
1	896	2770
2	3137	2758
3	4901	2758
4	4836	2758

prune6.4s (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1045	7	1052
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	1047	7	1054

Error

0.9b

Counts

1054 → 7

Alt Table

Status	Error	Program
	2.9b	(.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 (neg.f64 z) 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)))))
	3.2b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) 2)))) (cbrt.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)))))
	2.3b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.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 (-.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)))))
	36.5b	(.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 (+.f64 1 (sqrt.f64 z)) (-.f64 1 (sqrt.f64 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)))))
	2.9b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 (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)))))
▶	2.2b	(.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 2076511864126339/4000000000000 (.f64 z z)))) (/.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)))))
	2.8b	(.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 (exp.f64 (-.f64 1 z)) (exp.f64 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 141694 to 119222 computations (15.9% saved)

localize96.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 2076511864126339/4000000000000 (.f64 z z)))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 3))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 4))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 5))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 6))) (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 7))) (/.f64 3764081837873279/25000000000000000000000 (+.f64 (-.f64 (-.f64 1 z) 1) 8))))
	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
	1.9b	(.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))))
	4.5b	(-.f64 (-.f64 1 z) 1)

series64.0ms (0%)

Counts

1 → 12

Calls

1 calls:

63.0ms

(*.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (*.f64 2076511864126339/4000000000000 (*.f64 z z)))) (/.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))))

rewrite619.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`frac-add_binary64`
114×	`frac-times_binary64`
89×	`associate-*r/_binary64`
49×	`flip-+_binary64`
49×	`flip3-+_binary64`

Counts

1 → 137

Calls

1 calls:

242.0ms

(*.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (*.f64 2076511864126339/4000000000000 (*.f64 z z)))) (/.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))))

simplify1.8s (1.2%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
329×	`*-commutative_binary64`
250×	`associate-+l+_binary64`
210×	`associate-l_binary64`
196×	`distribute-rgt-in_binary64`

Counts

149 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	629	56016
1	2831	53796
2	4894	53792
3	4931	53792

prune8.6s (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1049	3	1052
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	1053	6	1059

Error

0.2b

Counts

1059 → 6

Alt Table

Status	Error	Program
✓	2.2b	(.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 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 2076511864126339/4000000000000 (.f64 z z)))) (/.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)))))
	2.6b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 (-.f64 1 z) 1/2))) (/.f64 (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000)))))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000)))))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (.f64 (+.f64 (-.f64 1 z) 3) (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))))) (.f64 (+.f64 (-.f64 1 z) 4) (fma.f64 -883075145810703/5000000000000 (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000)))) (.f64 (+.f64 (-.f64 1 z) 3) (fma.f64 7713234287776531/10000000000000 (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 229927536162678489561743043378339801/100000000000000000000000000000000 (.f64 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000)) (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000)))))))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (.f64 (+.f64 (-.f64 1 z) 3) (.f64 (+.f64 (-.f64 1 z) 2) (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))))))))))) (exp.f64 (+.f64 (-.f64 1 z) 13/2)))) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 2076511864126339/4000000000000 (*.f64 z z)))) (+.f64 (-.f64 (-.f64 1 z) 1) 3)) (+.f64 (-.f64 (-.f64 1 z) 1) 4)) (+.f64 (-.f64 (-.f64 1 z) 1) 5)) (+.f64 (-.f64 (-.f64 1 z) 1) 6)) (+.f64 (-.f64 (-.f64 1 z) 1) 7)) (+.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 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))) (.f64 (+.f64 (-.f64 1 z) 7) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) 3) (pow.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) 3))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 1 z) 13/2)) (exp.f64 (+.f64 (-.f64 1 z) 13/2))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))))))))))
	2.0b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (-.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3)))))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (-.f64 1 z) 6) (fma.f64 -3464277381643003/25000000000000000 (.f64 (+.f64 (-.f64 1 z) 4) (-.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3)))) (.f64 (+.f64 (-.f64 1 z) 5) (fma.f64 2501468655737381/200000000000000 (-.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (.f64 (+.f64 (-.f64 1 z) 4) (-.f64 (.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2)))) (/.f64 (/.f64 779821713148594364211109354209/25000000000000000000000000 (+.f64 (-.f64 1 z) 3)) (+.f64 (-.f64 1 z) 3))))))) (.f64 2496092394504893/250000000000000000000 (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (-.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3)))))))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 1 z) 13/2)) (exp.f64 (+.f64 (-.f64 1 z) 13/2))) (.f64 (+.f64 (-.f64 1 z) 7) (.f64 (+.f64 (-.f64 1 z) 6) (.f64 (+.f64 (-.f64 1 z) 5) (.f64 (+.f64 (-.f64 1 z) 4) (-.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))))))))))
	2.8b	(.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 (exp.f64 (-.f64 1 z)) (exp.f64 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)))))
	2.3b	(.f64 (/.f64 (PI.f64) (sin.f64 (.f64 (PI.f64) z))) (.f64 (exp.f64 (+.f64 (+.f64 z -15/2) (log.f64 (.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 (-.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 177303 to 143724 computations (18.9% saved)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))
✓	0.9b	(.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))
✓	1.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))) (.f64 (+.f64 (-.f64 1 z) 7) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) 3) (pow.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) 3))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 1 z) 13/2)) (exp.f64 (+.f64 (-.f64 1 z) 13/2))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))))))

series183.0ms (0.1%)

Counts

4 → 28

Calls

4 calls:

171.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))) (.f64 (+.f64 (-.f64 1 z) 7) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) 3) (pow.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) 3))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 1 z) 13/2)) (exp.f64 (+.f64 (-.f64 1 z) 13/2))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))))))
6.0ms	(.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))
5.0ms	(/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))
0.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

rewrite856.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

1394×	`*-un-lft-identity_binary64`
785×	`distribute-lft-out_binary64`
336×	`prod-diff_binary64`
273×	`times-frac_binary64`
222×	`add-sqr-sqrt_binary64`

Counts

4 → 553

Calls

4 calls:

178.0ms	(.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))
57.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (+.f64 (-.f64 1 z) 13/2) (-.f64 1 z))) (fma.f64 3764081837873279/25000000000000000000000 (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))) (.f64 (+.f64 (-.f64 1 z) 7) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) 3) (pow.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) 3))))) (.f64 (.f64 (sqrt.f64 (+.f64 (-.f64 1 z) 13/2)) (exp.f64 (+.f64 (-.f64 1 z) 13/2))) (.f64 (+.f64 (-.f64 1 z) 7) (fma.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5))) (.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (-.f64 (/.f64 2496092394504893/250000000000000000000 (+.f64 (-.f64 1 z) 6)) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 479507597606835099/10000000000000000 (fma.f64 z 904338909853211/2500000000000 (.f64 (*.f64 z z) 2076511864126339/4000000000000))) (/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))) (/.f64 -883075145810703/5000000000000 (+.f64 (-.f64 1 z) 3))) (/.f64 2501468655737381/200000000000000 (+.f64 (-.f64 1 z) 4))) (/.f64 -3464277381643003/25000000000000000 (+.f64 (-.f64 1 z) 5)))))))))
12.0ms	(/.f64 7713234287776531/10000000000000 (+.f64 (-.f64 1 z) 2))
2.0ms	(sqrt.f64 (*.f64 2 (PI.f64)))

simplify3.6s (2.4%)

Algorithm

1×	egg-herbie

Rules

707×	`associate-/l*_binary64`
591×	`fma-def_binary64`
352×	`*-commutative_binary64`
121×	`associate-r_binary64`
120×	`sub-neg_binary64`

Counts

581 → 452

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	999	155916
1	3137	106631
2	5482	106631

prune33.2s (22.1%)

Compiler: Compiled 518118 to 422084 computations (18.5% saved)

Details

analyze4.7s (3.2%)

sample1.5min (59.4%)

simplify77.0ms (0.1%)

prune25.0ms (0%)

localize105.0ms (0.1%)

series71.0ms (0%)

rewrite161.0ms (0.1%)

simplify187.0ms (0.1%)

prune6.4s (4.3%)

localize96.0ms (0.1%)

series64.0ms (0%)

rewrite619.0ms (0.4%)

simplify1.8s (1.2%)

prune8.6s (5.8%)

localize75.0ms (0.1%)

series183.0ms (0.1%)

rewrite856.0ms (0.6%)

simplify3.6s (2.4%)

prune33.2s (22.1%)

Profiling