Details

analyze875.0ms (5.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample44.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	44×	body	2048	valid
8.0ms	159×	body	128	valid
5.0ms	26×	body	1024	valid
2.0ms	15×	body	512	valid
2.0ms	7×	body	4096	valid
1.0ms	21×	body	128	nan
1.0ms	11×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify312.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (307.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (0%)

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

Error

37.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite192.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

36.9b

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`pow1_binary64_1162` `distribute-lft-out_binary64_1052`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip3--_binary64_1105` `sqrt-div_binary64_1118` `flip--_binary64_1076` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/l/_binary64_1048`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `sum-log_binary64_1192` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 1903 to 971 computations (49% saved)

series1.1s (6.7%)

Error

6.3b

Counts

4 → 76

Calls

4 calls:

306.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
240.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
230.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
226.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2847 to 2280 computations (19.9% saved)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5033	3065

prune170.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	141	7	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	7	149

Error

6.1b

Counts

149 → 7

Compiler

Compiled 2218 to 1227 computations (44.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.4b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite316.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

66×	`times-frac_binary64_1107`
59×	`add-sqr-sqrt_binary64_1123`
44×	`*-un-lft-identity_binary64_1101`
30×	`add-cube-cbrt_binary64_1136`
27×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
14×	`difference-of-squares_binary64_1070`
13×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046`
10×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r/_binary64_1047`
9×	`associate-/r*_binary64_1045`
7×	`flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053`
6×	`add-log-exp_binary64_1140` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067`
5×	`pow1_binary64_1162`
2×	`sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `diff-log_binary64_1193` `sub-neg_binary64_1094`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4703 to 2367 computations (49.7% saved)

series1.6s (10.1%)

Error

6.1b

Counts

4 → 75

Calls

4 calls:

557.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
512.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
244.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
231.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4038 to 3017 computations (25.3% saved)

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	6413
1	4945	6413

prune272.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	211	7	218

Error

6.1b

Counts

218 → 7

Compiler

Compiled 4415 to 2353 computations (46.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite195.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

39×	`add-sqr-sqrt_binary64_1123`
28×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
11×	`sqrt-prod_binary64_1117`
10×	`difference-of-squares_binary64_1070`
8×	`add-log-exp_binary64_1140`
7×	`cancel-sign-sub-inv_binary64_1067`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
4×	`flip3--_binary64_1105` `flip--_binary64_1076`
3×	`associate-/l*_binary64_1046`
2×	`sqrt-div_binary64_1118` `diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/r/_binary64_1047`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 88

Calls

4 calls:

8.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2534 to 1439 computations (43.2% saved)

series1.2s (7.4%)

Error

6.1b

Counts

4 → 74

Calls

4 calls:

424.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
239.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
235.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
217.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3448 to 2842 computations (17.6% saved)

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4988	3656
1	4988	3656

prune185.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	162	7	169

Error

6.1b

Counts

169 → 7

Compiler

Compiled 2726 to 1650 computations (39.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
24.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite150.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`pow1_binary64_1162` `distribute-lft-out_binary64_1052`
4×	`associate-/r*_binary64_1045`
3×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046`
2×	`flip3--_binary64_1105` `sqrt-div_binary64_1118` `flip--_binary64_1076` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/r/_binary64_1047`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `sum-log_binary64_1192` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2033 to 1101 computations (45.8% saved)

series1.1s (7%)

Error

6.1b

Counts

4 → 74

Calls

4 calls:

368.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
235.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
232.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
222.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3183 to 2573 computations (19.2% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5046	3028

prune149.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	144	9	153

Error

6.1b

Counts

153 → 9

Compiler

Compiled 2277 to 1310 computations (42.5% saved)

regimes5.9s (37%)

Accuracy

Total 1.2b remaining (18.6%)

Threshold costs 0b (0%)

Compiler

Compiled 32258 to 25504 computations (20.9% saved)

bsearch94.0ms (0.6%)

Steps

Iters	Range	Point
5	1.600789070947133e+106	2.0885041693244802e+111	7.357075075270595e+109
10	1.172920430121053e-218	5.476788882336384e-205	6.5744603722298956e-217
1	-1.642455628083301e+138	-2.6752393369196204e+133	-6.632227499857312e+135

Iters

Range

Point

1.600789070947133e+106

2.0885041693244802e+111

7.357075075270595e+109

1.172920430121053e-218

5.476788882336384e-205

6.5744603722298956e-217

-1.642455628083301e+138

-2.6752393369196204e+133

-6.632227499857312e+135

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	98
1	116	98

end3.0ms (0%)

Compiler: Compiled 66 to 45 computations (31.8% saved)

sample1.8s (11.1%)

Algorithm

1×

intervals

Results

321.0ms	1176×	body	2048	valid
307.0ms	730×	body	1024	valid
290.0ms	5207×	body	128	valid
137.0ms	392×	body	4096	valid
53.0ms	319×	body	512	valid
37.0ms	656×	body	128	nan
21.0ms	176×	body	256	valid
20.0ms	366×	body	128	invalid

Compiler

Compiled 267 to 219 computations (18% saved)

Details

analyze875.0ms (5.5%)

sample44.0ms (0.3%)

simplify312.0ms (2%)

prune7.0ms (0%)

localize11.0ms (0.1%)

rewrite192.0ms (1.2%)

series1.1s (6.7%)

simplify64.0ms (0.4%)

prune170.0ms (1.1%)

localize13.0ms (0.1%)

rewrite316.0ms (2%)

series1.6s (10.1%)

simplify118.0ms (0.7%)

prune272.0ms (1.7%)

localize15.0ms (0.1%)

rewrite195.0ms (1.2%)

series1.2s (7.4%)

simplify56.0ms (0.4%)

prune185.0ms (1.2%)

localize13.0ms (0.1%)

rewrite150.0ms (0.9%)

series1.1s (7%)

simplify48.0ms (0.3%)

prune149.0ms (0.9%)

regimes5.9s (37%)

bsearch94.0ms (0.6%)

simplify4.0ms (0%)

end3.0ms (0%)

sample1.8s (11.1%)

Profiling