Details

analyze1.3s (4.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample234.0ms (0.7%)

Algorithm

1×

intervals

Results

71.0ms	131×	body	1024	valid
64.0ms	121×	body	1024	nan
28.0ms	67×	body	512	valid
21.0ms	57×	body	512	nan
16.0ms	15×	body	2048	valid
8.0ms	33×	body	256	nan
6.0ms	24×	body	256	valid
3.0ms	19×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

62.5b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
1.0b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
4.8b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64` `unpow-prod-down_binary64`
11×	`sqr-pow_binary64` `add-cbrt-cube_binary64`
10×	`distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
13.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series1.2s (3.9%)

Counts

4 → 12

Calls

4 calls:

913.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
259.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
59.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
18.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify141.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4959	9948
1	4959	9948

prune600.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	5	167

Error

1.7b

Counts

167 → 5

Compiler

Compiled 9392 to 6464 computations (31.2% saved)

localize246.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
2.0b	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

rewrite81.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
14×	`pow1_binary64`
9×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`log-prod_binary64`
6×	`pow-pow_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
2×	`div-exp_binary64`
1×	`log-pow_binary64` `div-inv_binary64` `log-div_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4944	3514
1	4944	3514

prune3.7s (11.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Error

1.7b

Counts

79 → 5

Compiler

Compiled 36246 to 26748 computations (26.2% saved)

localize249.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
3.0b	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))
3.0b	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))

rewrite97.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`log-prod_binary64`
26×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
12×	`pow1_binary64` `add-exp-log_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `div-inv_binary64` `log-div_binary64`

Counts

4 → 88

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))
4.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))
0.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

simplify85.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4949	4116
1	4949	4116

prune4.9s (15.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Error

1.7b

Counts

97 → 5

Compiler

Compiled 45698 to 33804 computations (26% saved)

localize264.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
3.0b	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))

rewrite90.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`log-prod_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
14×	`pow1_binary64` `add-exp-log_binary64`
13×	`cbrt-prod_binary64`
9×	`pow-unpow_binary64` `times-frac_binary64`
6×	`pow-pow_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
2×	`log-pow_binary64`
1×	`cbrt-div_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `div-inv_binary64` `log-div_binary64`

Counts

4 → 78

Calls

4 calls:

5.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (cbrt.f64 (/.f64 4 PI.f64)))
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5182	1009

prune4.4s (13.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

1.7b

Counts

87 → 5

Compiler

Compiled 40346 to 29974 computations (25.7% saved)

regimes1.9s (6%)

Accuracy

Total 0.5b remaining (20.5%)

Threshold costs 0.5b (20.5%)

Compiler

Compiled 33144 to 24602 computations (25.8% saved)

bsearch0.0ms (0%)

simplify28.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	1023	815
1	1023	815

end0.0ms (0%)

sample12.1s (37.8%)

Algorithm

1×

intervals

Results

2.2s	3961×	body	1024	valid
2.0s	3901×	body	1024	nan
774.0ms	1957×	body	512	valid
718.0ms	1922×	body	512	nan
552.0ms	499×	body	2048	valid
261.0ms	950×	body	256	valid
247.0ms	1003×	body	256	nan
89.0ms	633×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	2×	body	128	nan

Compiler

Compiled 6015 to 4468 computations (25.7% saved)

Details

analyze1.3s (4.2%)

sample234.0ms (0.7%)

simplify83.0ms (0.3%)

prune8.0ms (0%)

localize24.0ms (0.1%)

rewrite64.0ms (0.2%)

series1.2s (3.9%)

simplify141.0ms (0.4%)

prune600.0ms (1.9%)

localize246.0ms (0.8%)

rewrite81.0ms (0.3%)

series0.0ms (0%)

simplify74.0ms (0.2%)

prune3.7s (11.6%)

localize249.0ms (0.8%)

rewrite97.0ms (0.3%)

series0.0ms (0%)

simplify85.0ms (0.3%)

prune4.9s (15.3%)

localize264.0ms (0.8%)

rewrite90.0ms (0.3%)

series0.0ms (0%)

simplify62.0ms (0.2%)

prune4.4s (13.6%)

regimes1.9s (6%)

bsearch0.0ms (0%)

simplify28.0ms (0.1%)

end0.0ms (0%)

sample12.1s (37.8%)

Profiling