Details

analyze545.0ms (4.5%)

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
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)

sample43.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	37×	body	2048	valid
8.0ms	156×	body	128	valid
7.0ms	22×	body	4096	valid
4.0ms	21×	body	1024	valid
2.0ms	15×	body	512	valid
1.0ms	16×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify532.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (423.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

35.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite173.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`pow1_binary64_821` `distribute-lft-out_binary64_711`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 72

Calls

4 calls:

14.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series893.0ms (7.3%)

Error

5.4b

Counts

4 → 76

Calls

4 calls:

248.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
185.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
181.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
171.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3466 to 2621 computations (24.4% saved)

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5033	3065

prune186.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	139	9	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Error

5.3b

Counts

149 → 9

Compiler

Compiled 3155 to 1673 computations (47% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite315.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

66×	`times-frac_binary64_766`
59×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760`
30×	`add-cube-cbrt_binary64_795`
27×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`difference-of-squares_binary64_729`
13×	`sqrt-prod_binary64_776` `associate-/l*_binary64_705`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/r/_binary64_706`
9×	`associate-/r*_binary64_704`
7×	`flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out--_binary64_712`
6×	`add-log-exp_binary64_799` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `div-inv_binary64_757` `cancel-sign-sub-inv_binary64_726`
5×	`pow1_binary64_821`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `diff-log_binary64_852` `sub-neg_binary64_753`

Counts

4 → 136

Calls

4 calls:

24.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
21.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.0ms	(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)))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series1.2s (9.9%)

Error

5.3b

Counts

4 → 74

Calls

4 calls:

334.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
327.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
239.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
200.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 4503 to 3219 computations (28.5% saved)

simplify151.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5011	6202

prune333.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	211	8	219

Error

5.3b

Counts

219 → 8

Compiler

Compiled 6055 to 3134 computations (48.2% 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))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite176.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

39×	`add-sqr-sqrt_binary64_782`
28×	`*-un-lft-identity_binary64_760`
18×	`add-cube-cbrt_binary64_795` `times-frac_binary64_766`
11×	`sqrt-prod_binary64_776`
10×	`difference-of-squares_binary64_729`
8×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-/r*_binary64_704`
5×	`pow1_binary64_821` `distribute-lft-out--_binary64_712`
4×	`flip3--_binary64_764` `flip--_binary64_735`
3×	`associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `associate-/r/_binary64_706`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 88

Calls

4 calls:

11.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2944 to 1670 computations (43.3% saved)

series937.0ms (7.7%)

Error

5.3b

Counts

4 → 75

Calls

4 calls:

289.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
197.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
196.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
165.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 4209 to 3329 computations (20.9% saved)

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4956	3671
1	4956	3671

prune254.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Error

5.3b

Counts

171 → 8

Compiler

Compiled 4242 to 2523 computations (40.5% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite174.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

18×	`add-exp-log_binary64_798`
14×	`add-sqr-sqrt_binary64_782`
13×	`add-cbrt-cube_binary64_796`
11×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
8×	`add-log-exp_binary64_799`
7×	`sqrt-prod_binary64_776` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811`
5×	`pow1_binary64_821`
4×	`prod-exp_binary64_809` `cbrt-undiv_binary64_794`
3×	`flip3--_binary64_764` `flip--_binary64_735` `times-frac_binary64_766` `associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `difference-of-squares_binary64_729` `1-exp_binary64_804` `cbrt-unprod_binary64_793`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `distribute-lft-out--_binary64_712` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-r/_binary64_702` `associate-/r/_binary64_706` `associate-/r_binary64_704`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2450 to 1516 computations (38.1% saved)

series1000.0ms (8.2%)

Error

5.3b

Counts

4 → 75

Calls

4 calls:

359.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
191.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
178.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
157.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 4459 to 3581 computations (19.7% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	2981
1	4962	2981

prune190.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	147	9	156

Error

5.3b

Counts

156 → 9

Compiler

Compiled 3618 to 2277 computations (37.1% saved)

regimes1.2s (9.9%)

Accuracy

Total 1.8b remaining (24%)

Threshold costs 0b (0%)

Compiler

Compiled 7024 to 5354 computations (23.8% saved)

bsearch122.0ms (1%)

Steps

Iters	Range	Point
11	2.6703851346995524e+126	1.8161627452327913e+151	1.556115004665923e+145
7	1.292389771899446e-102	2.841453316854276e-101	1.3082309990435538e-102
8	-9.709253565025955e+61	-1.8407022634408423e+57	-7.026086903474302e+61

Iters

Range

Point

2.6703851346995524e+126

1.8161627452327913e+151

1.556115004665923e+145

1.292389771899446e-102

2.841453316854276e-101

1.3082309990435538e-102

-9.709253565025955e+61

-1.8407022634408423e+57

-7.026086903474302e+61

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	97	89
1	97	89

end0.0ms (0%)

sample3.4s (27.9%)

Algorithm

1×

intervals

Results

347.0ms	1096×	body	2048	valid
320.0ms	5234×	body	128	valid
166.0ms	695×	body	1024	valid
151.0ms	406×	body	4096	valid
72.0ms	394×	body	512	valid
42.0ms	687×	body	128	nan
22.0ms	386×	body	128	invalid
21.0ms	175×	body	256	valid

Compiler

Compiled 1866 to 1413 computations (24.3% saved)

Details

analyze545.0ms (4.5%)

sample43.0ms (0.4%)

simplify532.0ms (4.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite173.0ms (1.4%)

series893.0ms (7.3%)

simplify86.0ms (0.7%)

prune186.0ms (1.5%)

localize14.0ms (0.1%)

rewrite315.0ms (2.6%)

series1.2s (9.9%)

simplify151.0ms (1.2%)

prune333.0ms (2.7%)

localize15.0ms (0.1%)

rewrite176.0ms (1.4%)

series937.0ms (7.7%)

simplify92.0ms (0.8%)

prune254.0ms (2.1%)

localize25.0ms (0.2%)

rewrite174.0ms (1.4%)

series1000.0ms (8.2%)

simplify82.0ms (0.7%)

prune190.0ms (1.6%)

regimes1.2s (9.9%)

bsearch122.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (27.9%)

Profiling