Details

analyze748.0ms (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
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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	174×	body	128	valid
11.0ms	35×	body	2048	valid
6.0ms	14×	body	4096	valid
4.0ms	13×	body	1024	valid
4.0ms	15×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify574.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (464.0ms)

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

32.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
6×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`pow1_binary64_139`
4×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
3×	`distribute-lft-out--_binary64_30`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `sub-neg_binary64_71`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `pow1/2_binary64_158`

Counts

4 → 74

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series410.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
103.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
87.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune148.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	9	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Error

5.0b

Counts

87 → 9

Compiler

Compiled 2143 to 1181 computations (44.9% 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)))))
3.1b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
8.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite93.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`times-frac_binary64_84`
21×	`*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
12×	`add-sqr-sqrt_binary64_100`
11×	`add-cube-cbrt_binary64_113` `associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `flip3-+_binary64_81`
3×	`sqrt-prod_binary64_94`
2×	`frac-2neg_binary64_89` `sqrt-div_binary64_95` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `associate-/l/_binary64_25` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 102

Calls

4 calls:

28.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
25.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
11.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series720.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
219.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
109.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
84.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4959	3121
1	4959	3121

prune200.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Error

5.0b

Counts

123 → 8

Compiler

Compiled 3266 to 1858 computations (43.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.4b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
8×	`add-log-exp_binary64_117`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`associate-/r*_binary64_22`
3×	`sqrt-prod_binary64_94` `associate-/l*_binary64_23`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 72

Calls

4 calls:

12.0ms	(+.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))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series376.0ms (4%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
89.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
73.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
41.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify171.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4896	1972
1	4896	1972

prune153.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	84	8	92

Error

5.0b

Counts

92 → 8

Compiler

Compiled 2264 to 1298 computations (42.7% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

7.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
9.4b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
22.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-prod_binary64_94` `add-log-exp_binary64_117` `pow1_binary64_139`
4×	`sqrt-div_binary64_95`
3×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `associate-/r/_binary64_24` `pow1/2_binary64_158` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 66

Calls

4 calls:

16.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))

series581.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
119.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
89.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5065	1846

prune138.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	78	8	86

Error

5.0b

Counts

86 → 8

Compiler

Compiled 2862 to 1599 computations (44.1% saved)

regimes1.1s (11.9%)

Accuracy

Total 1.0b remaining (15.3%)

Threshold costs 1.0b (15.3%)

Compiler

Compiled 3744 to 2808 computations (25% saved)

bsearch146.0ms (1.6%)

Steps

Iters	Range	Point
7	2.7321536462493888e+138	1.4149561378808454e+140	5.425482410905856e+139
10	-5.337491136382482e-303	1.235746678865531e-301	-2.647768469823155e-306
7	-3.5625938568282703e+93	-2.7211723544719877e+91	-2.587685883918172e+93

Iters

Range

Point

2.7321536462493888e+138

1.4149561378808454e+140

5.425482410905856e+139

-5.337491136382482e-303

1.235746678865531e-301

-2.647768469823155e-306

-3.5625938568282703e+93

-2.7211723544719877e+91

-2.587685883918172e+93

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	105	82
1	105	82

end0.0ms (0%)

sample3.1s (33.7%)

Algorithm

1×

intervals

Results

442.0ms	5251×	body	128	valid
428.0ms	1068×	body	2048	valid
219.0ms	445×	body	4096	valid
217.0ms	687×	body	1024	valid
91.0ms	387×	body	512	valid
53.0ms	670×	body	128	nan
31.0ms	381×	body	128	invalid
25.0ms	162×	body	256	valid

Compiler

Compiled 1028 to 758 computations (26.3% saved)

Details

analyze748.0ms (8%)

sample50.0ms (0.5%)

simplify574.0ms (6.2%)

prune4.0ms (0%)

localize18.0ms (0.2%)

rewrite44.0ms (0.5%)

series410.0ms (4.4%)

simplify136.0ms (1.5%)

prune148.0ms (1.6%)

localize13.0ms (0.1%)

rewrite93.0ms (1%)

series720.0ms (7.7%)

simplify99.0ms (1.1%)

prune200.0ms (2.2%)

localize19.0ms (0.2%)

rewrite40.0ms (0.4%)

series376.0ms (4%)

simplify171.0ms (1.8%)

prune153.0ms (1.6%)

localize34.0ms (0.4%)

rewrite55.0ms (0.6%)

series581.0ms (6.3%)

simplify89.0ms (1%)

prune138.0ms (1.5%)

regimes1.1s (11.9%)

bsearch146.0ms (1.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (33.7%)

Profiling