Details

analyze469.0ms (8.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	37×	body	2048	valid
9.0ms	169×	body	128	valid
4.0ms	22×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	34×	body	128	nan
2.0ms	10×	body	512	valid
1.0ms	6×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify368.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms (0.1%)

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

Merged error: 30.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_5215`
14×	`*-un-lft-identity_binary64_5193`
9×	`add-cbrt-cube_binary64_5229` `add-exp-log_binary64_5231`
8×	`add-cube-cbrt_binary64_5228` `add-log-exp_binary64_5232`
6×	`associate-/l*_binary64_5138` `difference-of-squares_binary64_5162` `times-frac_binary64_5199` `sqrt-prod_binary64_5209`
5×	`pow1_binary64_5254`
4×	`flip3--_binary64_5197` `flip--_binary64_5168` `cancel-sign-sub-inv_binary64_5159`
3×	`distribute-lft-out--_binary64_5145`
2×	`sqrt-div_binary64_5210` `sub-neg_binary64_5186` `cbrt-undiv_binary64_5227` `div-exp_binary64_5244` `associate-/l/_binary64_5140` `diff-log_binary64_5285`
1×	`pow1/2_binary64_5273` `div-sub_binary64_5198` `div-inv_binary64_5190` `clear-num_binary64_5192` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206` `prod-exp_binary64_5242` `associate-/r*_binary64_5137` `cbrt-unprod_binary64_5226` `frac-2neg_binary64_5204`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series268.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4893	1983
1	4893	1983

prune130.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 4.5b

Counts

87 → 11

Compiler

Compiled 2189 to 1324 computations (39.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_5215`
10×	`pow1_binary64_5254`
9×	`add-cbrt-cube_binary64_5229` `*-un-lft-identity_binary64_5193` `add-exp-log_binary64_5231`
8×	`add-log-exp_binary64_5232`
7×	`add-cube-cbrt_binary64_5228`
4×	`cancel-sign-sub-inv_binary64_5159` `sqrt-prod_binary64_5209`
3×	`flip3--_binary64_5197` `pow-prod-down_binary64_5264` `flip--_binary64_5168` `associate-r_binary64_5133` `prod-exp_binary64_5242` `cbrt-unprod_binary64_5226`
2×	`sqrt-div_binary64_5210` `sub-neg_binary64_5186` `difference-of-squares_binary64_5162` `diff-log_binary64_5285`
1×	`distribute-lft-out--_binary64_5145` `associate-l_binary64_5134` `pow1/2_binary64_5273` `*-commutative_binary64_5124` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series171.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
14.0ms	(.f64 (.f64 3 a) c)

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune81.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 4.5b

Counts

85 → 11

Compiler

Compiled 1764 to 1077 computations (38.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
1.2b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
18.4b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_5215`
14×	`*-un-lft-identity_binary64_5193`
9×	`add-cbrt-cube_binary64_5229` `add-exp-log_binary64_5231`
8×	`add-cube-cbrt_binary64_5228` `add-log-exp_binary64_5232`
6×	`associate-/l*_binary64_5138` `difference-of-squares_binary64_5162` `times-frac_binary64_5199` `sqrt-prod_binary64_5209`
5×	`pow1_binary64_5254`
3×	`distribute-lft-out--_binary64_5145` `cancel-sign-sub-inv_binary64_5159`
2×	`flip3--_binary64_5197` `sqrt-div_binary64_5210` `flip--_binary64_5168` `flip-+_binary64_5167` `cbrt-undiv_binary64_5227` `flip3-+_binary64_5196` `div-exp_binary64_5244` `associate-/l/_binary64_5140`
1×	`sub-neg_binary64_5186` `sum-log_binary64_5284` `pow1/2_binary64_5273` `div-sub_binary64_5198` `div-inv_binary64_5190` `clear-num_binary64_5192` `+-commutative_binary64_5123` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206` `diff-log_binary64_5285` `prod-exp_binary64_5242` `associate-/r*_binary64_5137` `cbrt-unprod_binary64_5226` `frac-2neg_binary64_5204`

Counts

4 → 73

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
4.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

series275.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
70.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
60.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))
32.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	1969
1	4994	1969

prune96.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	85	11	96

Merged error: 4.5b

Counts

96 → 11

Compiler

Compiled 2141 to 1293 computations (39.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_5215`
10×	`pow1_binary64_5254`
9×	`add-cbrt-cube_binary64_5229` `*-un-lft-identity_binary64_5193` `add-exp-log_binary64_5231`
8×	`add-log-exp_binary64_5232`
7×	`add-cube-cbrt_binary64_5228`
4×	`cancel-sign-sub-inv_binary64_5159` `sqrt-prod_binary64_5209`
3×	`flip3--_binary64_5197` `pow-prod-down_binary64_5264` `flip--_binary64_5168` `associate-r_binary64_5133` `prod-exp_binary64_5242` `cbrt-unprod_binary64_5226`
2×	`sqrt-div_binary64_5210` `sub-neg_binary64_5186` `difference-of-squares_binary64_5162` `diff-log_binary64_5285`
1×	`distribute-lft-out--_binary64_5145` `associate-l_binary64_5134` `pow1/2_binary64_5273` `*-commutative_binary64_5124` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series170.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
14.0ms	(.f64 (.f64 3 a) c)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune77.0ms (1.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	73	12	85

Merged error: 4.5b

Counts

85 → 12

Compiler

Compiled 1717 to 1073 computations (37.5% saved)

regimes812.0ms (15%)

Compiler: Compiled 4721 to 3646 computations (22.8% saved)

bsearch53.0ms (1%)

Steps

Iters	Range		Point
7	1.5905821695811115e-50	2.0896905838181703e-48	7.334233368061974e-50
8	-2.0922019410616626e+112	-1.82358309996822e+109	-3.1102062341024787e+111

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	59
1	109	59

end0.0ms (0%)

sample2.0s (36.2%)

Algorithm

1×

intervals

Results

284.0ms	5243×	body	128	valid
275.0ms	1087×	body	2048	valid
144.0ms	721×	body	1024	valid
128.0ms	396×	body	4096	valid
59.0ms	370×	body	512	valid
39.0ms	695×	body	128	nan
22.0ms	423×	body	128	invalid
20.0ms	183×	body	256	valid

Compiler

Compiled 901 to 693 computations (23.1% saved)

Details

analyze469.0ms (8.6%)

sample41.0ms (0.8%)

simplify368.0ms (6.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series268.0ms (4.9%)

simplify89.0ms (1.6%)

prune130.0ms (2.4%)

localize11.0ms (0.2%)

rewrite26.0ms (0.5%)

series171.0ms (3.1%)

simplify65.0ms (1.2%)

prune81.0ms (1.5%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series275.0ms (5.1%)

simplify61.0ms (1.1%)

prune96.0ms (1.8%)

localize13.0ms (0.2%)

rewrite27.0ms (0.5%)

series170.0ms (3.1%)

simplify63.0ms (1.2%)

prune77.0ms (1.4%)

regimes812.0ms (15%)

bsearch53.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.0s (36.2%)

Profiling