Details

analyze418.0ms (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)

sample56.0ms (0.6%)

Algorithm

1×

intervals

Results

41.0ms	243×	body	256	valid
3.0ms	32×	body	128	nan
1.0ms	13×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify328.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (228.0ms)

Iter	Nodes	Cost
0	4834	48
1	4834	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

Error

34.4b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.5b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_3169`
11×	`cbrt-prod_binary64_3178`
10×	`*-un-lft-identity_binary64_3147`
9×	`sqrt-prod_binary64_3163`
8×	`add-cube-cbrt_binary64_3182`
6×	`times-frac_binary64_3153` `pow1_binary64_3208`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `difference-of-squares_binary64_3116` `add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
2×	`cbrt-div_binary64_3179` `flip--_binary64_3122` `pow1/3_binary64_3229` `flip3--_binary64_3151` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`associate-*l/_binary64_3090` `distribute-lft-out--_binary64_3099` `div-inv_binary64_3144`

Counts

4 → 61

Calls

4 calls:

12.0ms	(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 (11.2%)

Counts

4 → 38

Calls

4 calls:

484.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
393.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
82.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
61.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2701 to 2173 computations (19.5% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4897	2039
1	4897	2039

prune192.0ms (2.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	82	17	99
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	18	101

Error

29.0b

Counts

101 → 18

Compiler

Compiled 4245 to 1600 computations (62.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (.f64 g g) (.f64 h h))
9.5b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_3169` `sqrt-prod_binary64_3163`
6×	`*-un-lft-identity_binary64_3147` `pow1_binary64_3208` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164`
3×	`flip--_binary64_3122` `flip3--_binary64_3151` `difference-of-squares_binary64_3116`
2×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`cbrt-div_binary64_3179` `pow1/3_binary64_3229` `cancel-sign-sub-inv_binary64_3113` `associate-*l/_binary64_3090` `sub-neg_binary64_3140` `diff-log_binary64_3239` `cbrt-prod_binary64_3178`

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	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series651.0ms (7.2%)

Counts

4 → 39

Calls

4 calls:

404.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
107.0ms	(-.f64 (.f64 g g) (.f64 h h))
77.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
62.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2360 to 1881 computations (20.3% saved)

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4897	1371
1	4897	1371

prune155.0ms (1.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	93	19	112

Error

27.8b

Counts

112 → 19

Compiler

Compiled 4045 to 1565 computations (61.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (.f64 g g) (.f64 h h))
2.8b	(-.f64 (.f64 g g) (.f64 h h))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186` `sqrt-prod_binary64_3163`
6×	`*-un-lft-identity_binary64_3147` `pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
4×	`flip--_binary64_3122` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `flip3--_binary64_3151` `difference-of-squares_binary64_3116` `sqrt-div_binary64_3164`
2×	`cancel-sign-sub-inv_binary64_3113` `sub-neg_binary64_3140` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `diff-log_binary64_3239`

Counts

4 → 58

Calls

4 calls:

5.0ms	(-.f64 (.f64 g g) (.f64 h h))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series373.0ms (4.1%)

Counts

4 → 42

Calls

4 calls:

116.0ms	(-.f64 (.f64 g g) (.f64 h h))
110.0ms	(-.f64 (.f64 g g) (.f64 h h))
80.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
67.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2226 to 1754 computations (21.2% saved)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	1222
1	4939	1222

prune171.0ms (1.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	98	21	119

Error

27.8b

Counts

119 → 21

Compiler

Compiled 4425 to 1721 computations (61.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(-.f64 (.f64 g g) (.f64 h h))
9.5b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.1b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_3169` `sqrt-prod_binary64_3163`
6×	`*-un-lft-identity_binary64_3147` `pow1_binary64_3208` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164`
3×	`flip--_binary64_3122` `flip3--_binary64_3151` `difference-of-squares_binary64_3116`
2×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`cbrt-div_binary64_3179` `pow1/3_binary64_3229` `cancel-sign-sub-inv_binary64_3113` `associate-*l/_binary64_3090` `sub-neg_binary64_3140` `diff-log_binary64_3239` `cbrt-prod_binary64_3178`

Counts

4 → 55

Calls

4 calls:

10.0ms	(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)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series648.0ms (7.1%)

Counts

4 → 39

Calls

4 calls:

398.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
101.0ms	(-.f64 (.f64 g g) (.f64 h h))
86.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
63.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Compiler

Compiled 2360 to 1881 computations (20.3% saved)

simplify121.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4897	1371
1	4897	1371

prune117.0ms (1.3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	92	23	115

Error

27.8b

Counts

115 → 23

Compiler

Compiled 3257 to 1124 computations (65.5% saved)

regimes1.0s (11.4%)

Accuracy

Total 1.3b remaining (4%)

Threshold costs 0b (0%)

Compiler

Compiled 15278 to 9049 computations (40.8% saved)

bsearch96.0ms (1.1%)

Steps

Iters	Range		Point
11	1.9140540134873396e-147	4.2305109813310524e-125	1.9367400249629983e-147

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	79	117
1	79	117

end0.0ms (0%)

sample3.2s (35.4%)

Algorithm

1×

intervals

Results

1.4s	7544×	body	256	valid
98.0ms	1227×	body	128	nan
38.0ms	456×	body	128	valid

Compiler

Compiled 2280 to 1346 computations (41% saved)

Details

analyze418.0ms (4.6%)

sample56.0ms (0.6%)

simplify328.0ms (3.6%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

rewrite38.0ms (0.4%)

series1.0s (11.2%)

simplify83.0ms (0.9%)

prune192.0ms (2.1%)

localize19.0ms (0.2%)

rewrite29.0ms (0.3%)

series651.0ms (7.2%)

simplify124.0ms (1.4%)

prune155.0ms (1.7%)

localize20.0ms (0.2%)

rewrite24.0ms (0.3%)

series373.0ms (4.1%)

simplify72.0ms (0.8%)

prune171.0ms (1.9%)

localize22.0ms (0.2%)

rewrite30.0ms (0.3%)

series648.0ms (7.1%)

simplify121.0ms (1.3%)

prune117.0ms (1.3%)

regimes1.0s (11.4%)

bsearch96.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (35.4%)

Profiling