Details

analyze864.0ms (4.6%)

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)

sample82.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	37×	body	2048	valid
15.0ms	156×	body	128	valid
13.0ms	22×	body	4096	valid
8.0ms	21×	body	1024	valid
4.0ms	15×	body	512	valid
1.0ms	16×	body	128	nan
1.0ms	13×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify797.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (644.0ms)

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

35.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize23.0ms (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))))

rewrite261.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

24×	`*-un-lft-identity_binary64_1783`
15×	`add-sqr-sqrt_binary64_1805`
14×	`add-cube-cbrt_binary64_1818`
12×	`times-frac_binary64_1789`
8×	`add-log-exp_binary64_1822`
6×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
5×	`pow1_binary64_1844` `distribute-lft-out_binary64_1734`
4×	`associate-/l*_binary64_1728`
3×	`sqrt-prod_binary64_1799` `associate-/r*_binary64_1727`
2×	`flip3--_binary64_1787` `sqrt-div_binary64_1800` `flip--_binary64_1758` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/l/_binary64_1730`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sum-log_binary64_1874` `+-commutative_binary64_1713` `diff-log_binary64_1875` `sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 72

Calls

4 calls:

16.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series1.3s (6.9%)

Error

5.4b

Counts

4 → 76

Calls

4 calls:

343.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
283.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
271.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
264.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 3466 to 2621 computations (24.4% saved)

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5033	3065

prune300.0ms (1.6%)

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)

localize30.0ms (0.2%)

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))))

rewrite467.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

66×	`times-frac_binary64_1789`
59×	`add-sqr-sqrt_binary64_1805`
44×	`*-un-lft-identity_binary64_1783`
30×	`add-cube-cbrt_binary64_1818`
27×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
14×	`difference-of-squares_binary64_1752`
13×	`sqrt-prod_binary64_1799` `associate-/l*_binary64_1728`
10×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-/r/_binary64_1729`
9×	`associate-/r*_binary64_1727`
7×	`flip3--_binary64_1787` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735`
6×	`add-log-exp_binary64_1822` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749`
5×	`pow1_binary64_1844`
2×	`sqrt-div_binary64_1800` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `associate-/l/_binary64_1730` `diff-log_binary64_1875` `sub-neg_binary64_1776`

Counts

4 → 136

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
23.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
13.0ms	(-.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))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series1.8s (9.4%)

Error

5.3b

Counts

4 → 74

Calls

4 calls:

555.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
500.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
287.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
276.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4503 to 3219 computations (28.5% saved)

simplify245.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	5011	6202

prune533.0ms (2.9%)

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)

localize33.0ms (0.2%)

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))))

rewrite274.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

39×	`add-sqr-sqrt_binary64_1805`
28×	`*-un-lft-identity_binary64_1783`
18×	`add-cube-cbrt_binary64_1818` `times-frac_binary64_1789`
11×	`sqrt-prod_binary64_1799`
10×	`difference-of-squares_binary64_1752`
8×	`add-log-exp_binary64_1822`
7×	`cancel-sign-sub-inv_binary64_1749`
6×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727`
5×	`pow1_binary64_1844` `distribute-lft-out--_binary64_1735`
4×	`flip3--_binary64_1787` `flip--_binary64_1758`
3×	`associate-/l*_binary64_1728`
2×	`sqrt-div_binary64_1800` `diff-log_binary64_1875` `sub-neg_binary64_1776` `associate-/r/_binary64_1729`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 88

Calls

4 calls:

15.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
13.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2944 to 1670 computations (43.3% saved)

series1.4s (7.4%)

Error

5.3b

Counts

4 → 75

Calls

4 calls:

421.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
282.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
273.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
266.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 4209 to 3329 computations (20.9% saved)

simplify160.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4956	3671
1	4956	3671

prune365.0ms (2%)

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)

localize34.0ms (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))))

rewrite237.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

18×	`add-exp-log_binary64_1821`
14×	`add-sqr-sqrt_binary64_1805`
13×	`add-cbrt-cube_binary64_1819`
11×	`*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
7×	`sqrt-prod_binary64_1799` `cancel-sign-sub-inv_binary64_1749` `div-exp_binary64_1834`
5×	`pow1_binary64_1844`
4×	`prod-exp_binary64_1832` `cbrt-undiv_binary64_1817`
3×	`flip3--_binary64_1787` `flip--_binary64_1758` `times-frac_binary64_1789` `associate-/l*_binary64_1728`
2×	`sqrt-div_binary64_1800` `diff-log_binary64_1875` `sub-neg_binary64_1776` `difference-of-squares_binary64_1752` `1-exp_binary64_1827` `cbrt-unprod_binary64_1816`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `distribute-lft-out--_binary64_1735` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-r/_binary64_1725` `associate-/r/_binary64_1729` `associate-/r_binary64_1727`

Counts

4 → 73

Calls

4 calls:

22.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
15.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2450 to 1516 computations (38.1% saved)

series1.6s (8.5%)

Error

5.3b

Counts

4 → 75

Calls

4 calls:

538.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
307.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
304.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
272.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4459 to 3581 computations (19.7% saved)

simplify150.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4962	2981
1	4962	2981

prune338.0ms (1.8%)

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)

regimes2.0s (10.5%)

Accuracy

Total 1.8b remaining (24%)

Threshold costs 0b (0%)

Compiler

Compiled 7024 to 5354 computations (23.8% saved)

bsearch189.0ms (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)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	97	89
1	97	89

end0.0ms (0%)

sample5.1s (27.4%)

Algorithm

1×

intervals

Results

542.0ms	1096×	body	2048	valid
483.0ms	5234×	body	128	valid
265.0ms	695×	body	1024	valid
259.0ms	406×	body	4096	valid
113.0ms	394×	body	512	valid
61.0ms	687×	body	128	nan
36.0ms	175×	body	256	valid
35.0ms	386×	body	128	invalid

Compiler

Compiled 1866 to 1413 computations (24.3% saved)

Details

analyze864.0ms (4.6%)

sample82.0ms (0.4%)

simplify797.0ms (4.3%)

prune7.0ms (0%)

localize23.0ms (0.1%)

rewrite261.0ms (1.4%)

series1.3s (6.9%)

simplify139.0ms (0.7%)

prune300.0ms (1.6%)

localize30.0ms (0.2%)

rewrite467.0ms (2.5%)

series1.8s (9.4%)

simplify245.0ms (1.3%)

prune533.0ms (2.9%)

localize33.0ms (0.2%)

rewrite274.0ms (1.5%)

series1.4s (7.4%)

simplify160.0ms (0.9%)

prune365.0ms (2%)

localize34.0ms (0.2%)

rewrite237.0ms (1.3%)

series1.6s (8.5%)

simplify150.0ms (0.8%)

prune338.0ms (1.8%)

regimes2.0s (10.5%)

bsearch189.0ms (1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample5.1s (27.4%)

Profiling