Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	63×	body	1024	valid
3.0ms	132×	body	128	valid
3.0ms	44×	body	512	valid
1.0ms	7×	body	2048	valid
0.0ms	10×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify101.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite61.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

30.6b

Rules

15×	`sqrt-prod_binary64_1799`
14×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
6×	`cancel-sign-sub-inv_binary64_1749`
5×	`add-cube-cbrt_binary64_1818`
4×	`add-log-exp_binary64_1822` `difference-of-squares_binary64_1752`
3×	`pow1_binary64_1844` `distribute-lft-out--_binary64_1735`
2×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `flip3-+_binary64_1786` `flip-+_binary64_1757` `rem-sqrt-square_binary64_1796`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 571 to 370 computations (35.2% saved)

series50.0ms (1.2%)

Error

30.4b

Counts

2 → 8

Calls

2 calls:

29.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 225 to 178 computations (20.9% saved)

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5272	570

prune42.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	3	49

Error

0.1b

Counts

49 → 3

Compiler

Compiled 557 to 366 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite112.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`*-un-lft-identity_binary64_1783`
24×	`sqrt-prod_binary64_1799`
21×	`distribute-lft-out_binary64_1734`
18×	`times-frac_binary64_1789`
16×	`add-sqr-sqrt_binary64_1805`
15×	`add-cube-cbrt_binary64_1818`
7×	`add-exp-log_binary64_1821`
6×	`associate-/r*_binary64_1727`
5×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/l*_binary64_1728`
2×	`div-exp_binary64_1834` `associate-/r/_binary64_1729` `sqrt-div_binary64_1800`
1×	`inv-pow_binary64_1868` `pow-flip_binary64_1857` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1268 to 926 computations (27% saved)

series54.0ms (1.3%)

Error

0.1b

Counts

3 → 11

Calls

3 calls:

17.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 246 to 215 computations (12.6% saved)

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5423	1208

prune88.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	10	89

Error

0.0b

Counts

89 → 10

Compiler

Compiled 1337 to 982 computations (26.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(cbrt.f64 (+.f64 1 x))

rewrite169.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
18×	`add-cube-cbrt_binary64_1818`
13×	`cbrt-prod_binary64_1814`
10×	`add-exp-log_binary64_1821` `associate-r_binary64_1723`
9×	`sqrt-prod_binary64_1799` `times-frac_binary64_1789`
8×	`add-cbrt-cube_binary64_1819`
7×	`pow1_binary64_1844`
6×	`cbrt-div_binary64_1815`
4×	`add-log-exp_binary64_1822` `flip3-+_binary64_1786` `flip-+_binary64_1757`
3×	`distribute-lft-out_binary64_1734` `unswap-sqr_binary64_1751` `associate-l_binary64_1724` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`pow1/3_binary64_1865` `sqrt-div_binary64_1800` `associate-*r/_binary64_1725` `div-exp_binary64_1834` `associate-/r/_binary64_1729`
1×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `1-exp_binary64_1827` `rec-exp_binary64_1833` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 90

Calls

4 calls:

11.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2392 to 1869 computations (21.9% saved)

series309.0ms (7.5%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

103.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
73.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
49.0ms	(cbrt.f64 (+.f64 1 x))
48.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1786 to 1527 computations (14.5% saved)

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4905	2561
1	4905	2561

prune168.0ms (4.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	117	10	127

Error

0.0b

Counts

127 → 10

Compiler

Compiled 2896 to 2235 computations (22.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
0.3b	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite264.0ms (6.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`cbrt-prod_binary64_1814`
43×	`add-sqr-sqrt_binary64_1805`
41×	`*-un-lft-identity_binary64_1783`
36×	`sqrt-prod_binary64_1799`
21×	`add-cube-cbrt_binary64_1818`
18×	`cbrt-div_binary64_1815`
16×	`sqrt-div_binary64_1800`
14×	`swap-sqr_binary64_1750`
11×	`pow1_binary64_1844`
10×	`associate-l_binary64_1724` `associate-r_binary64_1723`
9×	`pow1/3_binary64_1865` `flip3-+_binary64_1786` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `distribute-lft-out_binary64_1734`
6×	`add-exp-log_binary64_1821`
4×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `frac-times_binary64_1793`
2×	`pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `associate-l/_binary64_1726` `associate-r/_binary64_1725`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `*-commutative_binary64_1714`

Counts

4 → 117

Calls

4 calls:

18.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
4.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
4.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 3774 to 3037 computations (19.5% saved)

series253.0ms (6.1%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

53.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
52.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))
51.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 x)))
45.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2166 to 1842 computations (15% saved)

simplify102.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4834	2374
1	4834	2374

prune236.0ms (5.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	149	10	159

Error

0.0b

Counts

159 → 10

Compiler

Compiled 4120 to 3242 computations (21.3% saved)

regimes180.0ms (4.3%)

Accuracy

Total 0.1b remaining (90.7%)

Threshold costs 0.1b (90.7%)

Compiler

Compiled 2114 to 1701 computations (19.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.7s (40.2%)

Algorithm

1×

intervals

Results

200.0ms	1948×	body	1024	valid
120.0ms	4291×	body	128	valid
81.0ms	1002×	body	512	valid
27.0ms	213×	body	2048	valid
27.0ms	546×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 1042 to 840 computations (19.4% saved)

Details

analyze3.0ms (0.1%)

sample21.0ms (0.5%)

simplify101.0ms (2.4%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

rewrite61.0ms (1.5%)

series50.0ms (1.2%)

simplify54.0ms (1.3%)

prune42.0ms (1%)

localize6.0ms (0.1%)

rewrite112.0ms (2.7%)

series54.0ms (1.3%)

simplify92.0ms (2.2%)

prune88.0ms (2.1%)

localize10.0ms (0.2%)

rewrite169.0ms (4.1%)

series309.0ms (7.5%)

simplify77.0ms (1.9%)

prune168.0ms (4.1%)

localize13.0ms (0.3%)

rewrite264.0ms (6.4%)

series253.0ms (6.1%)

simplify102.0ms (2.5%)

prune236.0ms (5.7%)

regimes180.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (40.2%)

Profiling