Details

analyze417.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 38 to 24 computations (36.8% saved)

sample56.0ms (0.8%)

Algorithm

1×

intervals

Results

40.0ms	236×	body	256	valid
3.0ms	35×	body	128	nan
2.0ms	20×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify337.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (245.0ms)

Iter	Nodes	Cost
0	4834	48
1	4834	48

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 37.3b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.6b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2487`
11×	`cbrt-prod_binary64_2496`
10×	`*-un-lft-identity_binary64_2465`
9×	`sqrt-prod_binary64_2481`
8×	`add-cube-cbrt_binary64_2500`
6×	`times-frac_binary64_2471` `pow1_binary64_2526`
4×	`difference-of-squares_binary64_2434` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `cbrt-div_binary64_2497` `pow1/3_binary64_2547` `rem-sqrt-square_binary64_2478` `flip3--_binary64_2469` `sqrt-pow1_binary64_2483`
1×	`associate-*l/_binary64_2408` `distribute-lft-out--_binary64_2417` `div-inv_binary64_2462`

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series540.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
239.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
29.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5115	1656

prune171.0ms (2.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	53	20	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	20	75

Merged error: 33.0b

Counts

75 → 20

Compiler

Compiled 3549 to 1370 computations (61.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
6×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`difference-of-squares_binary64_2434` `flip--_binary64_2440` `flip3--_binary64_2469`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`associate-*l/_binary64_2408` `cbrt-div_binary64_2497` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `cbrt-prod_binary64_2496`

Counts

4 → 55

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series338.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
33.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
32.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
22.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4981	1104
1	4981	1104

prune137.0ms (1.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	66	21	87

Merged error: 32.1b

Counts

87 → 21

Compiler

Compiled 3280 to 1317 computations (59.8% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
31.0b	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-div_binary64_2482`
8×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `add-sqr-sqrt_binary64_2487`
5×	`*-un-lft-identity_binary64_2465` `sqrt-prod_binary64_2481` `flip--_binary64_2440` `add-cube-cbrt_binary64_2500` `flip3--_binary64_2469`
4×	`frac-times_binary64_2475` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`flip3-+_binary64_2468` `associate-*l/_binary64_2408` `flip-+_binary64_2439` `sqrt-pow1_binary64_2483`
2×	`difference-of-squares_binary64_2434` `pow1/2_binary64_2545` `associate-*r/_binary64_2407`
1×	`cbrt-div_binary64_2497` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `pow-prod-down_binary64_2536` `cbrt-prod_binary64_2496`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
6.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series347.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
38.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
22.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5159	1281

prune136.0ms (1.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	70	21	91

Merged error: 32.1b

Counts

91 → 21

Compiler

Compiled 3466 to 1411 computations (59.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
6×	`*-un-lft-identity_binary64_2465` `add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`difference-of-squares_binary64_2434` `flip--_binary64_2440` `flip3--_binary64_2469`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`associate-*l/_binary64_2408` `cbrt-div_binary64_2497` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `cbrt-prod_binary64_2496`

Counts

4 → 55

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series330.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
30.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
24.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4981	1104
1	4981	1104

prune93.0ms (1.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	67	21	88

Merged error: 32.1b

Counts

88 → 21

Compiler

Compiled 2463 to 859 computations (65.1% saved)

regimes1.0s (13.8%)

Compiler: Compiled 15019 to 9063 computations (39.7% saved)

bsearch100.0ms (1.3%)

Steps

Iters	Range		Point
11	3.0019519371863446e-168	1.256773250423451e-143	2.2719417431808843e-159

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	97
1	82	97

end0.0ms (0%)

sample2.9s (38.9%)

Algorithm

1×

intervals

Results

1.2s	7559×	body	256	valid
101.0ms	1233×	body	128	nan
39.0ms	441×	body	128	valid

Compiler

Compiled 2009 to 1218 computations (39.4% saved)

Details

analyze417.0ms (5.6%)

sample56.0ms (0.8%)

simplify337.0ms (4.5%)

prune9.0ms (0.1%)

localize17.0ms (0.2%)

rewrite34.0ms (0.5%)

series540.0ms (7.2%)

simplify62.0ms (0.8%)

prune171.0ms (2.3%)

localize19.0ms (0.3%)

rewrite28.0ms (0.4%)

series338.0ms (4.5%)

simplify85.0ms (1.1%)

prune137.0ms (1.8%)

localize28.0ms (0.4%)

rewrite30.0ms (0.4%)

series347.0ms (4.7%)

simplify73.0ms (1%)

prune136.0ms (1.8%)

localize19.0ms (0.3%)

rewrite30.0ms (0.4%)

series330.0ms (4.4%)

simplify88.0ms (1.2%)

prune93.0ms (1.2%)

regimes1.0s (13.8%)

bsearch100.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (38.9%)

Profiling