Details

analyze463.0ms (7.8%)

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)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
8.0ms	35×	body	2048	valid
4.0ms	20×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify422.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (259.0ms)

Iter	Nodes	Cost
0	1707	24
1	1707	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: 33.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite36.0ms (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:

13.0ms	(/.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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series511.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
60.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6789	1967

prune123.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.1b

Counts

83 → 10

Compiler

Compiled 2074 to 1257 computations (39.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
8.7b	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite52.0ms (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:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
13.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series893.0ms (15%)

Counts

4 → 12

Calls

4 calls:

365.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
280.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5567	3147

prune144.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 5.1b

Counts

124 → 11

Compiler

Compiled 3297 to 2023 computations (38.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_1123`
13×	`add-cbrt-cube_binary64_1121`
9×	`div-exp_binary64_1136` `*-un-lft-identity_binary64_1088`
8×	`add-sqr-sqrt_binary64_1109` `add-log-exp_binary64_1124` `pow1_binary64_1146`
7×	`add-cube-cbrt_binary64_1120`
6×	`prod-exp_binary64_1134`
5×	`associate-/r/_binary64_1036`
4×	`cbrt-undiv_binary64_1119`
3×	`rec-exp_binary64_1135` `times-frac_binary64_1094` `sqrt-prod_binary64_1103` `1-exp_binary64_1129` `flip-+_binary64_1062` `flip3-+_binary64_1091` `associate-/l*_binary64_1035`
2×	`associate-*l/_binary64_1033` `cbrt-unprod_binary64_1118` `flip3--_binary64_1092` `frac-times_binary64_1098` `flip--_binary64_1063` `sqrt-div_binary64_1104` `pow-flip_binary64_1159`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `inv-pow_binary64_1170` `rem-sqrt-square_binary64_1101` `associate-/r_binary64_1034` `sub-neg_binary64_1081` `sum-log_binary64_1176` `+-commutative_binary64_1020` `diff-log_binary64_1177` `pow-prod-down_binary64_1156` `distribute-lft-out_binary64_1041` `sqrt-pow1_binary64_1105` `associate-r/_binary64_1032` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

4 → 75

Calls

4 calls:

15.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series579.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

268.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5194	1852

prune102.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	87	11	98

Merged error: 5.1b

Counts

98 → 11

Compiler

Compiled 2107 to 1309 computations (37.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1109`
10×	`pow1_binary64_1146`
9×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
8×	`add-log-exp_binary64_1124` `*-un-lft-identity_binary64_1088`
6×	`add-cube-cbrt_binary64_1120`
4×	`sqrt-prod_binary64_1103`
3×	`associate-r_binary64_1030` `cbrt-unprod_binary64_1118` `flip3--_binary64_1092` `flip--_binary64_1063` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134`
2×	`sub-neg_binary64_1081` `sqrt-div_binary64_1104` `diff-log_binary64_1177` `difference-of-squares_binary64_1057`
1×	`-commutative_binary64_1021` `rem-sqrt-square_binary64_1101` `associate-l*_binary64_1031` `sqrt-pow1_binary64_1105` `distribute-lft-out--_binary64_1042` `pow1/2_binary64_1165`

Counts

4 → 58

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series327.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
30.0ms	(.f64 (.f64 3 a) c)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4939	1210
1	4939	1210

prune71.0ms (1.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	69	12	81

Merged error: 5.0b

Counts

81 → 12

Compiler

Compiled 1502 to 889 computations (40.8% saved)

regimes240.0ms (4%)

Compiler: Compiled 833 to 707 computations (15.1% saved)

bsearch106.0ms (1.8%)

Steps

Iters	Range	Point
8	6.64275593550351e+97	2.5210146164357893e+102	1.7374191487467014e+101
10	2.23400780941565e-159	2.330746391411611e-144	2.2617122697789544e-159
7	-1.6249009059312762e+154	-2.69477264842752e+152	-3.6161208674775763e+152

Iters

Range

Point

6.64275593550351e+97

2.5210146164357893e+102

1.7374191487467014e+101

2.23400780941565e-159

2.330746391411611e-144

2.2617122697789544e-159

-1.6249009059312762e+154

-2.69477264842752e+152

-3.6161208674775763e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	126	98
1	126	98

end0.0ms (0%)

sample1.5s (24.6%)

Algorithm

1×

intervals

Results

292.0ms	1152×	body	2048	valid
275.0ms	5095×	body	128	valid
164.0ms	782×	body	1024	valid
131.0ms	418×	body	4096	valid
58.0ms	377×	body	512	valid
35.0ms	666×	body	128	nan
20.0ms	380×	body	128	invalid
18.0ms	176×	body	256	valid

Compiler

Compiled 277 to 221 computations (20.2% saved)

Details

analyze463.0ms (7.8%)

sample39.0ms (0.7%)

simplify422.0ms (7.1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite36.0ms (0.6%)

series511.0ms (8.6%)

simplify73.0ms (1.2%)

prune123.0ms (2.1%)

localize15.0ms (0.2%)

rewrite52.0ms (0.9%)

series893.0ms (15%)

simplify57.0ms (1%)

prune144.0ms (2.4%)

localize13.0ms (0.2%)

rewrite38.0ms (0.6%)

series579.0ms (9.7%)

simplify73.0ms (1.2%)

prune102.0ms (1.7%)

localize10.0ms (0.2%)

rewrite30.0ms (0.5%)

series327.0ms (5.5%)

simplify54.0ms (0.9%)

prune71.0ms (1.2%)

regimes240.0ms (4%)

bsearch106.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (24.6%)

Profiling