Details

analyze412.0ms (4.6%)

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)

sample57.0ms (0.6%)

Algorithm

1×

intervals

Results

41.0ms	246×	body	256	valid
3.0ms	41×	body	128	nan
1.0ms	10×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify363.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (194.0ms)

Iter	Nodes	Cost
0	4882	48
1	4882	48

prune6.0ms (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: 34.1b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
8.1b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite35.0ms (0.4%)

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:

10.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.0s (11.8%)

Counts

4 → 12

Calls

4 calls:

465.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
461.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
62.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
59.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4956	1656
1	4956	1656

prune165.0ms (1.9%)

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: 29.5b

Counts

75 → 20

Compiler

Compiled 3547 to 1363 computations (61.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(-.f64 (.f64 g g) (.f64 h h))
7.5b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2487`
10×	`*-un-lft-identity_binary64_2465` `cbrt-prod_binary64_2496`
9×	`sqrt-prod_binary64_2481`
8×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504` `times-frac_binary64_2471` `pow1_binary64_2526`
5×	`difference-of-squares_binary64_2434`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`flip--_binary64_2440` `flip3--_binary64_2469`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`cbrt-div_binary64_2497` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `diff-log_binary64_2557`

Counts

4 → 64

Calls

4 calls:

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

series617.0ms (7%)

Counts

4 → 12

Calls

4 calls:

463.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
58.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
56.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
40.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4908	1501
1	4908	1501

prune144.0ms (1.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	73	23	96

Merged error: 28.9b

Counts

96 → 23

Compiler

Compiled 3749 to 1489 computations (60.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.6b	(-.f64 (.f64 g g) (.f64 h h))
7.5b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
27.3b	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2487`
10×	`sqrt-div_binary64_2482` `cbrt-prod_binary64_2496`
9×	`*-un-lft-identity_binary64_2465`
8×	`pow1_binary64_2526`
7×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504` `times-frac_binary64_2471` `sqrt-prod_binary64_2481`
5×	`flip--_binary64_2440` `flip3--_binary64_2469`
4×	`difference-of-squares_binary64_2434` `frac-times_binary64_2475` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `sqrt-pow1_binary64_2483`
2×	`associate-l/_binary64_2408` `pow1/2_binary64_2545` `associate-r/_binary64_2407`
1×	`cbrt-div_binary64_2497` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `pow1/3_binary64_2547` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `pow-prod-down_binary64_2536`

Counts

4 → 67

Calls

4 calls:

9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
8.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series657.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

468.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
84.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
64.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
39.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5138	1678

prune148.0ms (1.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	21	22
Picked	1	0	1
Done	0	0	0
Total	79	23	102

Merged error: 28.9b

Counts

102 → 23

Compiler

Compiled 3940 to 1583 computations (59.8% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 g (sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h))))
3.6b	(-.f64 (.f64 g g) (.f64 h h))
27.3b	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
27.3b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-div_binary64_2482`
8×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`sqrt-prod_binary64_2481` `flip--_binary64_2440` `add-cube-cbrt_binary64_2500` `flip3--_binary64_2469`
4×	`flip3-+_binary64_2468` `frac-times_binary64_2475` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`sqrt-pow1_binary64_2483`
2×	`associate-l/_binary64_2408` `difference-of-squares_binary64_2434` `pow1/2_binary64_2545` `associate-r/_binary64_2407`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(+.f64 g (sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h))))

series456.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(-.f64 (.f64 g g) (.f64 h h))
89.0ms	(+.f64 g (sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h))))
76.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
57.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4968	1125
1	4968	1125

prune108.0ms (1.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	5	17	22
Picked	1	0	1
Done	0	0	0
Total	73	22	95

Merged error: 28.5b

Counts

95 → 22

Compiler

Compiled 2727 to 967 computations (64.5% saved)

regimes1.1s (12.1%)

Compiler: Compiled 16483 to 9630 computations (41.6% saved)

bsearch175.0ms (2%)

Steps

Iters	Range		Point
9	7.588556056449843e+92	1.021209113772303e+99	7.692507907003283e+92
10	-3.361487268442452e-214	-3.686667256690219e-227	-3.322449351468917e-214

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	85	182
1	85	182

end0.0ms (0%)

sample3.0s (33.4%)

Algorithm

1×

intervals

Results

1.2s	7557×	body	256	valid
106.0ms	1241×	body	128	nan
39.0ms	443×	body	128	valid

Compiler

Compiled 2257 to 1306 computations (42.1% saved)

Details

analyze412.0ms (4.6%)

sample57.0ms (0.6%)

simplify363.0ms (4.1%)

prune6.0ms (0.1%)

localize18.0ms (0.2%)

rewrite35.0ms (0.4%)

series1.0s (11.8%)

simplify54.0ms (0.6%)

prune165.0ms (1.9%)

localize20.0ms (0.2%)

rewrite30.0ms (0.3%)

series617.0ms (7%)

simplify71.0ms (0.8%)

prune144.0ms (1.6%)

localize27.0ms (0.3%)

rewrite35.0ms (0.4%)

series657.0ms (7.4%)

simplify63.0ms (0.7%)

prune148.0ms (1.7%)

localize28.0ms (0.3%)

rewrite29.0ms (0.3%)

series456.0ms (5.1%)

simplify69.0ms (0.8%)

prune108.0ms (1.2%)

regimes1.1s (12.1%)

bsearch175.0ms (2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (33.4%)

Profiling