Details

analyze1.4s (7.7%)

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)

sample70.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	168×	body	128	valid
12.0ms	28×	body	2048	valid
11.0ms	32×	body	1024	valid
5.0ms	9×	body	4096	valid
3.0ms	11×	body	512	valid
3.0ms	31×	body	128	nan
1.0ms	8×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify608.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (598.0ms)

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

32.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize21.0ms (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)
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite263.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

31.9b

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:

18.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
12.0ms	(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)))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series1.2s (6.6%)

Error

5.9b

Counts

4 → 72

Calls

4 calls:

335.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
268.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
258.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
234.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3213 to 2441 computations (24% saved)

simplify123.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5257	2816

prune272.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Error

5.8b

Counts

145 → 12

Compiler

Compiled 3045 to 1607 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.8b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite455.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

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:

25.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
21.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
12.0ms	(-.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))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series1.7s (9.1%)

Error

5.8b

Counts

4 → 71

Calls

4 calls:

542.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
482.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
263.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
253.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4275 to 3059 computations (28.4% saved)

simplify215.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5009	6020

prune429.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	209	10	219

Error

5.8b

Counts

219 → 10

Compiler

Compiled 5927 to 3043 computations (48.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite421.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

102×	`times-frac_binary64_1789`
82×	`*-un-lft-identity_binary64_1783`
57×	`add-sqr-sqrt_binary64_1805`
56×	`add-cube-cbrt_binary64_1818`
18×	`associate-/r*_binary64_1727`
15×	`add-exp-log_binary64_1821`
13×	`distribute-lft-out_binary64_1734`
9×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729`
8×	`add-log-exp_binary64_1822`
7×	`div-exp_binary64_1834`
6×	`pow1_binary64_1844`
5×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `div-inv_binary64_1780`
3×	`sqrt-prod_binary64_1799` `cbrt-undiv_binary64_1817` `associate-/l*_binary64_1728`
2×	`flip3--_binary64_1787` `sqrt-div_binary64_1800` `flip--_binary64_1758` `1-exp_binary64_1827` `rec-exp_binary64_1833`
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` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 135

Calls

4 calls:

24.0ms	(/.f64 1 (/.f64 a (+.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)))))
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 4590 to 2591 computations (43.6% saved)

series1.3s (6.9%)

Error

5.8b

Counts

4 → 72

Calls

4 calls:

353.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
281.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
270.0ms	(+.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))))

Compiler

Compiled 3483 to 2713 computations (22.1% saved)

simplify192.0ms (1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4929	5302
1	4929	5302

prune413.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	207	10	217

Error

5.8b

Counts

217 → 10

Compiler

Compiled 5175 to 2851 computations (44.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite475.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

21×	`add-sqr-sqrt_binary64_1805`
18×	`*-un-lft-identity_binary64_1783`
13×	`add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
11×	`times-frac_binary64_1789`
9×	`add-cbrt-cube_binary64_1819`
8×	`add-log-exp_binary64_1822`
7×	`pow1_binary64_1844`
4×	`prod-exp_binary64_1832` `associate-l_binary64_1724`
3×	`sqrt-prod_binary64_1799` `flip3-+_binary64_1786` `flip-+_binary64_1757` `unswap-sqr_binary64_1751`
2×	`flip3--_binary64_1787` `sqrt-div_binary64_1800` `flip--_binary64_1758` `distribute-lft-out_binary64_1734` `div-exp_binary64_1834` `cbrt-unprod_binary64_1816` `frac-times_binary64_1793` `associate-*l/_binary64_1726`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sum-log_binary64_1874` `+-commutative_binary64_1713` `pow-prod-down_binary64_1854` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `un-div-inv_binary64_1781` `associate-r/_binary64_1725` `div-inv_binary64_1780` `-commutative_binary64_1714` `diff-log_binary64_1875` `sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749`

Counts

4 → 80

Calls

4 calls:

28.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
12.0ms	(+.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 2417 to 1345 computations (44.4% saved)

series1.2s (6.4%)

Error

5.8b

Counts

4 → 72

Calls

4 calls:

316.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
258.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
253.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
233.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3483 to 2720 computations (21.9% saved)

simplify150.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4968	2856
1	4968	2856

prune257.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	152	10	162

Error

5.8b

Counts

162 → 10

Compiler

Compiled 3134 to 1735 computations (44.6% saved)

regimes2.0s (10.9%)

Accuracy

Total 1.1b remaining (16.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7512 to 5482 computations (27% saved)

bsearch174.0ms (1%)

Steps

Iters	Range	Point
7	9.536573715997247e+107	2.272091706956965e+109	1.2510227225299573e+109
9	1.1761980487950557e-203	1.1901236388873502e-196	1.1519003584921026e-201
7	-5.222027993423419e+93	-4.515317171743753e+91	-5.110132017758097e+93

Iters

Range

Point

9.536573715997247e+107

2.272091706956965e+109

1.2510227225299573e+109

1.1761980487950557e-203

1.1901236388873502e-196

1.1519003584921026e-201

-5.222027993423419e+93

-4.515317171743753e+91

-5.110132017758097e+93

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	131	97
1	131	97

end0.0ms (0%)

sample5.0s (27.1%)

Algorithm

1×

intervals

Results

500.0ms	1101×	body	2048	valid
477.0ms	5242×	body	128	valid
270.0ms	741×	body	1024	valid
217.0ms	391×	body	4096	valid
90.0ms	348×	body	512	valid
62.0ms	685×	body	128	nan
37.0ms	383×	body	128	invalid
31.0ms	177×	body	256	valid

Compiler

Compiled 1993 to 1448 computations (27.3% saved)

Details

analyze1.4s (7.7%)

sample70.0ms (0.4%)

simplify608.0ms (3.3%)

prune7.0ms (0%)

localize21.0ms (0.1%)

rewrite263.0ms (1.4%)

series1.2s (6.6%)

simplify123.0ms (0.7%)

prune272.0ms (1.5%)

localize26.0ms (0.1%)

rewrite455.0ms (2.5%)

series1.7s (9.1%)

simplify215.0ms (1.2%)

prune429.0ms (2.3%)

localize24.0ms (0.1%)

rewrite421.0ms (2.3%)

series1.3s (6.9%)

simplify192.0ms (1%)

prune413.0ms (2.3%)

localize28.0ms (0.2%)

rewrite475.0ms (2.6%)

series1.2s (6.4%)

simplify150.0ms (0.8%)

prune257.0ms (1.4%)

regimes2.0s (10.9%)

bsearch174.0ms (1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample5.0s (27.1%)

Profiling