Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	68×	body	1024	valid
6.0ms	138×	body	128	valid
4.0ms	32×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

17.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

1.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
1.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite71.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_1805`
118×	`times-frac_binary64_1789`
113×	`*-un-lft-identity_binary64_1783`
72×	`sqrt-prod_binary64_1799`
54×	`add-cube-cbrt_binary64_1818`
27×	`cancel-sign-sub-inv_binary64_1749`
25×	`difference-of-squares_binary64_1752`
13×	`associate-/r*_binary64_1727` `distribute-lft-out--_binary64_1735`
11×	`add-exp-log_binary64_1821`
10×	`distribute-lft-out_binary64_1734`
7×	`add-cbrt-cube_binary64_1819` `div-inv_binary64_1780` `pow1_binary64_1844`
6×	`associate-/l*_binary64_1728` `pow-flip_binary64_1857`
5×	`add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `sqrt-div_binary64_1800` `div-exp_binary64_1834`
2×	`inv-pow_binary64_1868` `1-exp_binary64_1827` `flip-+_binary64_1757` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`flip3--_binary64_1787` `diff-log_binary64_1875` `frac-sub_binary64_1792` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

3 → 173

Calls

6 calls:

39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0ms	(/.f64 1 (sqrt.f64 x))

series57.0ms (0.9%)

Counts

3 → 10

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 234 to 204 computations (12.8% saved)

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5118	3109

prune283.0ms (4.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	172	11	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	11	184

Error

17.1b

Counts

184 → 11

Compiler

Compiled 3271 to 2437 computations (25.5% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

1.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
1.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1805`
38×	`sqrt-prod_binary64_1799`
34×	`*-un-lft-identity_binary64_1783`
12×	`difference-of-squares_binary64_1752`
11×	`add-cube-cbrt_binary64_1818`
10×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728` `add-exp-log_binary64_1821` `times-frac_binary64_1789`
9×	`distribute-lft-out--_binary64_1735`
7×	`associate-r_binary64_1723` `pow1_binary64_1844`
6×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724`
5×	`add-log-exp_binary64_1822`
4×	`associate-*r/_binary64_1725` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800` `unswap-sqr_binary64_1751`
3×	`pow-prod-down_binary64_1854`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `sqrt-unprod_binary64_1803` `div-inv_binary64_1780` `associate-/r_binary64_1727` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

3 → 97

Calls

6 calls:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series120.0ms (2%)

Counts

3 → 12

Calls

3 calls:

57.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
35.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
27.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 382 to 311 computations (18.6% saved)

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5675	1943

prune139.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	117	3	120

Error

0.2b

Counts

120 → 3

Compiler

Compiled 2191 to 1409 computations (35.7% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1783`
78×	`times-frac_binary64_1789`
55×	`sqrt-prod_binary64_1799`
47×	`add-sqr-sqrt_binary64_1805`
45×	`distribute-lft-out_binary64_1734`
39×	`add-cube-cbrt_binary64_1818`
32×	`add-exp-log_binary64_1821`
27×	`associate-/l*_binary64_1728`
20×	`add-cbrt-cube_binary64_1819`
14×	`div-exp_binary64_1834`
9×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729`
7×	`associate-/r_binary64_1727` `cbrt-undiv_binary64_1817` `associate-r*_binary64_1723`
6×	`flip-+_binary64_1757` `associate-l_binary64_1724` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
5×	`prod-exp_binary64_1832`
4×	`associate-*r/_binary64_1725` `div-inv_binary64_1780` `sqrt-div_binary64_1800` `unswap-sqr_binary64_1751`
3×	`cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `pow-prod-down_binary64_1854` `rec-exp_binary64_1833`
2×	`pow1/2_binary64_1863` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782`
1×	`associate-/l/_binary64_1730` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `sqrt-unprod_binary64_1803` `pow-flip_binary64_1857` `*-commutative_binary64_1714` `sum-log_binary64_1874`

Counts

4 → 166

Calls

8 calls:

21.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series117.0ms (1.9%)

Counts

4 → 15

Calls

4 calls:

49.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
29.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 386 to 331 computations (14.2% saved)

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune314.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Error

0.0b

Counts

184 → 9

Compiler

Compiled 4178 to 2889 computations (30.9% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite67.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1789`
159×	`*-un-lft-identity_binary64_1783`
156×	`add-sqr-sqrt_binary64_1805`
119×	`add-cube-cbrt_binary64_1818`
87×	`sqrt-prod_binary64_1799`
49×	`distribute-lft-out_binary64_1734`
21×	`associate-/l*_binary64_1728`
20×	`associate-/r/_binary64_1729`
19×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819`
12×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
11×	`associate-/r*_binary64_1727`
10×	`div-inv_binary64_1780`
9×	`pow1_binary64_1844`
8×	`div-exp_binary64_1834`
7×	`associate-r_binary64_1723`
6×	`associate-l_binary64_1724` `add-log-exp_binary64_1822`
4×	`sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `unswap-sqr_binary64_1751`
3×	`pow-prod-down_binary64_1854`
2×	`associate-*r/_binary64_1725` `1-exp_binary64_1827` `pow1/2_binary64_1863` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`associate-/l/_binary64_1730` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-flip_binary64_1857` `*-commutative_binary64_1714` `sum-log_binary64_1874`

Counts

4 → 252

Calls

8 calls:

17.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series136.0ms (2.2%)

Counts

4 → 21

Calls

4 calls:

47.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
36.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
26.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 510 to 439 computations (13.9% saved)

simplify163.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4896	9188
1	4896	9188

prune517.0ms (8.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	271	2	273
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	273	9	282

Error

Counts

282 → 9

Compiler

Compiled 7292 to 5209 computations (28.6% saved)

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	731	3023
1	731	3023

regimes193.0ms (3.1%)

Compiler: Compiled 1896 to 1519 computations (19.9% saved)

bsearch0.0ms (0%)

regimes36.0ms (0.6%)

Compiler: Compiled 234 to 202 computations (13.7% saved)

bsearch0.0ms (0%)

regimes39.0ms (0.6%)

Compiler: Compiled 152 to 133 computations (12.5% saved)

bsearch17.0ms (0.3%)

Steps

Iters	Range		Point
7	3300.8171630890365	98334.15580277613	72052.32713768836

Compiler

Compiled 1 to 1 computations (0% saved)

regimes35.0ms (0.6%)

Compiler: Compiled 137 to 121 computations (11.7% saved)

bsearch14.0ms (0.2%)

Steps

Iters	Range		Point
6	302.52702270046814	3300.8171630890365	3245.9374679211824

Compiler

Compiled 1 to 1 computations (0% saved)

regimes25.0ms (0.4%)

Compiler: Compiled 82 to 73 computations (11% saved)

bsearch20.0ms (0.3%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	0.37458255856936945

Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.3%)

Compiler: Compiled 41 to 39 computations (4.9% saved)

bsearch20.0ms (0.3%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	0.32594028805984276

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.3%)

Compiler: Compiled 29 to 29 computations (0% saved)

bsearch18.0ms (0.3%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	0.4840276672158045

Compiler

Compiled 1 to 1 computations (0% saved)

regimes13.0ms (0.2%)

Compiler: Compiled 11 to 14 computations (-27.3% saved)

bsearch17.0ms (0.3%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	1.0062406200728051

Compiler

Compiled 1 to 1 computations (0% saved)

regimes14.0ms (0.2%)

Accuracy

Total 0.3b remaining (98.7%)

Threshold costs 0.3b (98.7%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch30.0ms (0.5%)

Steps

Iters	Range		Point
7	4.134814286250324e+100	3.6283051363825227e+102	2.6706943098737903e+102

Compiler

Compiled 181 to 152 computations (16% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	96	270
1	96	270

end0.0ms (0%)

sample3.0s (49.1%)

Algorithm

1×

intervals

Results

352.0ms	2226×	body	1024	valid
175.0ms	4294×	body	128	valid
120.0ms	983×	body	512	valid
40.0ms	497×	body	256	valid

Compiler

Compiled 2101 to 1692 computations (19.5% saved)

Pareto

0.5677530117921159

Details

analyze2.0ms (0%)

sample28.0ms (0.5%)

simplify103.0ms (1.7%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite71.0ms (1.2%)

series57.0ms (0.9%)

simplify91.0ms (1.5%)

prune283.0ms (4.6%)

localize7.0ms (0.1%)

rewrite47.0ms (0.8%)

series120.0ms (2%)

simplify70.0ms (1.1%)

prune139.0ms (2.3%)

localize9.0ms (0.1%)

rewrite70.0ms (1.1%)

series117.0ms (1.9%)

simplify94.0ms (1.5%)

prune314.0ms (5.1%)

localize10.0ms (0.2%)

rewrite67.0ms (1.1%)

series136.0ms (2.2%)

simplify163.0ms (2.7%)

prune517.0ms (8.5%)

simplify50.0ms (0.8%)

regimes193.0ms (3.1%)

bsearch0.0ms (0%)

regimes36.0ms (0.6%)

bsearch0.0ms (0%)

regimes39.0ms (0.6%)

bsearch17.0ms (0.3%)

regimes35.0ms (0.6%)

bsearch14.0ms (0.2%)

regimes25.0ms (0.4%)

bsearch20.0ms (0.3%)

regimes20.0ms (0.3%)

bsearch20.0ms (0.3%)

regimes18.0ms (0.3%)

bsearch18.0ms (0.3%)

regimes13.0ms (0.2%)

bsearch17.0ms (0.3%)

regimes14.0ms (0.2%)

bsearch30.0ms (0.5%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.0s (49.1%)

Profiling