Details

analyze879.0ms (7.3%)

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)

sample74.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	40×	body	2048	valid
17.0ms	170×	body	128	valid
8.0ms	20×	body	1024	valid
5.0ms	8×	body	4096	valid
4.0ms	14×	body	512	valid
2.0ms	23×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify777.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (490.0ms)

Iter	Nodes	Cost
0	1707	24
1	1707	24

prune7.0ms (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: 35.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite75.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1109`
13×	`*-un-lft-identity_binary64_1088`
9×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
8×	`add-log-exp_binary64_1124`
7×	`add-cube-cbrt_binary64_1120`
6×	`times-frac_binary64_1094` `sqrt-prod_binary64_1103` `associate-/l*_binary64_1035` `difference-of-squares_binary64_1057`
5×	`pow1_binary64_1146`
4×	`flip3--_binary64_1092` `flip--_binary64_1063`
3×	`distribute-lft-out--_binary64_1042`
2×	`sub-neg_binary64_1081` `associate-/l/_binary64_1037` `div-exp_binary64_1136` `sqrt-div_binary64_1104` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `cbrt-unprod_binary64_1118` `associate-/r*_binary64_1034` `div-sub_binary64_1093` `prod-exp_binary64_1134` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

4 → 70

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series1.0s (8.4%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
250.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
223.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
135.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify137.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	6789	1967

prune253.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 6.1b

Counts

83 → 12

Compiler

Compiled 2230 to 1357 computations (39.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
2.6b	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
10.9b	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite104.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
22×	`times-frac_binary64_1094`
21×	`*-un-lft-identity_binary64_1088`
17×	`div-exp_binary64_1136` `cbrt-undiv_binary64_1119`
13×	`cbrt-unprod_binary64_1118` `prod-exp_binary64_1134`
12×	`add-sqr-sqrt_binary64_1109`
11×	`add-cube-cbrt_binary64_1120` `associate-/l*_binary64_1035`
6×	`associate-/r/_binary64_1036` `add-log-exp_binary64_1124`
5×	`associate-/r*_binary64_1034` `pow1_binary64_1146` `distribute-lft-out_binary64_1041`
4×	`flip-+_binary64_1062` `flip3-+_binary64_1091` `div-inv_binary64_1085`
3×	`sqrt-prod_binary64_1103`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `sqrt-div_binary64_1104`
1×	`rem-sqrt-square_binary64_1101` `flip3--_binary64_1092` `associate-/l/_binary64_1037` `sum-log_binary64_1176` `flip--_binary64_1063` `+-commutative_binary64_1020` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`

Counts

4 → 102

Calls

4 calls:

31.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
24.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series1.7s (14.1%)

Counts

4 → 12

Calls

4 calls:

709.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
535.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
232.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
226.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5567	3147

prune288.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 6.0b

Counts

126 → 10

Compiler

Compiled 3361 to 2064 computations (38.6% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite63.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1088`
9×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
8×	`add-sqr-sqrt_binary64_1109` `add-log-exp_binary64_1124`
7×	`add-cube-cbrt_binary64_1120`
5×	`pow1_binary64_1146`
4×	`associate-/r*_binary64_1034` `times-frac_binary64_1094`
3×	`sqrt-prod_binary64_1103` `distribute-lft-out_binary64_1041`
2×	`flip3--_binary64_1092` `flip--_binary64_1063` `associate-/r/_binary64_1036` `div-exp_binary64_1136` `sqrt-div_binary64_1104` `flip-+_binary64_1062` `cbrt-undiv_binary64_1119` `flip3-+_binary64_1091`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `cbrt-unprod_binary64_1118` `sub-neg_binary64_1081` `sum-log_binary64_1176` `+-commutative_binary64_1020` `diff-log_binary64_1177` `prod-exp_binary64_1134` `sqrt-pow1_binary64_1105` `associate-/l*_binary64_1035` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

4 → 63

Calls

4 calls:

21.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series1.2s (10.2%)

Counts

4 → 12

Calls

4 calls:

653.0ms	(/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))
225.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
220.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
134.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify178.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4886	1665
1	4886	1665

prune187.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 6.0b

Counts

85 → 11

Compiler

Compiled 2203 to 1465 computations (33.5% saved)

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1109`
9×	`sqrt-prod_binary64_1103` `*-un-lft-identity_binary64_1088`
7×	`pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
6×	`sqrt-div_binary64_1104` `add-log-exp_binary64_1124`
4×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
3×	`rem-sqrt-square_binary64_1101` `flip3--_binary64_1092` `flip--_binary64_1063` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
1×	`sum-log_binary64_1176` `+-commutative_binary64_1020` `flip-+_binary64_1062` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041`

Counts

4 → 57

Calls

4 calls:

13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series915.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
228.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
227.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
217.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4957	1382
1	4957	1382

prune283.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	11	80

Merged error: 6.0b

Counts

80 → 11

Compiler

Compiled 3819 to 2359 computations (38.2% saved)

regimes585.0ms (4.8%)

Compiler: Compiled 1074 to 862 computations (19.7% saved)

bsearch175.0ms (1.5%)

Steps

Iters	Range	Point
10	3.3247051461308957e+58	4.037443110488911e+75	3.376433332167536e+75
5	-1.4397385330750025e-302	-3.6802190818420765e-303	-7.818817745763073e-303
9	-2.277742040036469e+136	-6.470709428625851e+128	-2.1352611747204783e+136

Iters

Range

Point

3.3247051461308957e+58

4.037443110488911e+75

3.376433332167536e+75

-1.4397385330750025e-302

-3.6802190818420765e-303

-7.818817745763073e-303

-2.277742040036469e+136

-6.470709428625851e+128

-2.1352611747204783e+136

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	124	92
1	124	92

end0.0ms (0%)

sample2.7s (22.6%)

Algorithm

1×

intervals

Results

555.0ms	1159×	body	2048	valid
510.0ms	5198×	body	128	valid
276.0ms	700×	body	1024	valid
228.0ms	388×	body	4096	valid
110.0ms	385×	body	512	valid
61.0ms	659×	body	128	nan
38.0ms	390×	body	128	invalid
31.0ms	170×	body	256	valid

Compiler

Compiled 321 to 248 computations (22.7% saved)

Details

analyze879.0ms (7.3%)

sample74.0ms (0.6%)

simplify777.0ms (6.4%)

prune7.0ms (0.1%)

localize20.0ms (0.2%)

rewrite75.0ms (0.6%)

series1.0s (8.4%)

simplify137.0ms (1.1%)

prune253.0ms (2.1%)

localize28.0ms (0.2%)

rewrite104.0ms (0.9%)

series1.7s (14.1%)

simplify112.0ms (0.9%)

prune288.0ms (2.4%)

localize27.0ms (0.2%)

rewrite63.0ms (0.5%)

series1.2s (10.2%)

simplify178.0ms (1.5%)

prune187.0ms (1.5%)

localize43.0ms (0.4%)

rewrite59.0ms (0.5%)

series915.0ms (7.6%)

simplify107.0ms (0.9%)

prune283.0ms (2.3%)

regimes585.0ms (4.8%)

bsearch175.0ms (1.5%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.7s (22.6%)

Profiling