Details

analyze11.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample72.0ms (0.6%)

Algorithm

1×

intervals

Results

45.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify293.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	5050	41

prune7.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
1.0b	(sqrt.f64 PI.f64)

rewrite711.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

41×	`add-sqr-sqrt_binary64_1805`
39×	`add-exp-log_binary64_1821`
38×	`add-cbrt-cube_binary64_1819`
36×	`associate-l_binary64_1724`
35×	`pow1_binary64_1844`
31×	`times-frac_binary64_1789`
29×	`*-un-lft-identity_binary64_1783`
27×	`add-cube-cbrt_binary64_1818`
19×	`prod-exp_binary64_1832`
17×	`cbrt-unprod_binary64_1816`
14×	`sqrt-prod_binary64_1799` `associate-*l/_binary64_1726`
12×	`frac-add_binary64_1791`
10×	`pow-prod-down_binary64_1854`
7×	`associate-r_binary64_1723`
6×	`flip3-+_binary64_1786` `frac-times_binary64_1793` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `associate-*r/_binary64_1725` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846`
5×	`div-exp_binary64_1834`
4×	`add-log-exp_binary64_1822` `cbrt-undiv_binary64_1817`
3×	`*-commutative_binary64_1714`
2×	`div-inv_binary64_1780` `pow2_binary64_1864` `pow-sqr_binary64_1756`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `1-exp_binary64_1827` `rec-exp_binary64_1833` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `pow3_binary64_1866` `rem-3cbrt-lft_binary64_1808`

Counts

4 → 140

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 13127 to 4592 computations (65% saved)

series518.0ms (4.1%)

Error

0.1b

Counts

4 → 9

Calls

4 calls:

377.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
71.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
46.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1395 to 766 computations (45.1% saved)

simplify149.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4973	4621
1	4973	4621

prune452.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Error

Counts

151 → 5

Compiler

Compiled 9525 to 4372 computations (54.1% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
0.2b	(.f64 2/3 (.f64 x x))

rewrite328.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64_1805`
31×	`associate-r_binary64_1723`
21×	`add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783`
20×	`add-cube-cbrt_binary64_1818`
16×	`sqrt-prod_binary64_1799`
15×	`add-cbrt-cube_binary64_1819`
12×	`associate-l_binary64_1724`
11×	`pow1_binary64_1844` `unswap-sqr_binary64_1751` `times-frac_binary64_1789`
10×	`prod-exp_binary64_1832`
8×	`unpow-prod-down_binary64_1862`
6×	`cbrt-unprod_binary64_1816`
4×	`pow-prod-down_binary64_1854` `add-log-exp_binary64_1822` `*-commutative_binary64_1714` `sqr-pow_binary64_1755`
3×	`sqrt-div_binary64_1800`
2×	`flip3-+_binary64_1786` `frac-times_binary64_1793` `flip-+_binary64_1757` `associate-*l/_binary64_1726` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`associate-*r/_binary64_1725` `div-inv_binary64_1780`

Counts

4 → 108

Calls

4 calls:

16.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
8.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
6.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 4531 to 3082 computations (32% saved)

series625.0ms (5%)

Error

Counts

4 → 15

Calls

4 calls:

384.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
96.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
79.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
44.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 1346 to 1044 computations (22.4% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4904	3280
1	4904	3280

prune300.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Error

Counts

128 → 5

Compiler

Compiled 4808 to 3269 computations (32% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite287.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64_1805`
24×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
18×	`times-frac_binary64_1789`
16×	`add-exp-log_binary64_1821`
15×	`sqrt-prod_binary64_1799`
13×	`add-cbrt-cube_binary64_1819`
10×	`pow1_binary64_1844`
8×	`associate-r_binary64_1723`
6×	`associate-/r_binary64_1727` `prod-exp_binary64_1832` `associate-l*_binary64_1724`
4×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `unpow-prod-down_binary64_1862`
3×	`associate-/l*_binary64_1728` `pow-prod-down_binary64_1854`
2×	`associate-/l/_binary64_1730` `*-commutative_binary64_1714` `sqr-pow_binary64_1755`
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` `flip3-+_binary64_1786` `flip-+_binary64_1757` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 98

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
8.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4117 to 2554 computations (38% saved)

series566.0ms (4.5%)

Error

Counts

4 → 12

Calls

4 calls:

409.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
83.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
47.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1040 to 799 computations (23.2% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4996	3574
1	4996	3574

prune254.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	111	4	115

Error

Counts

115 → 4

Compiler

Compiled 4304 to 2696 computations (37.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x)))))))
0.3b	(/.f64 1 (/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x))))))))
1.0b	(sqrt.f64 PI.f64)

rewrite765.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

162×	`times-frac_binary64_1789`
100×	`add-sqr-sqrt_binary64_1805`
98×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
51×	`sqrt-prod_binary64_1799`
27×	`associate-/r*_binary64_1727`
22×	`add-exp-log_binary64_1821`
16×	`add-cbrt-cube_binary64_1819`
11×	`pow1_binary64_1844` `associate-/r/_binary64_1729`
9×	`associate-/l*_binary64_1728`
8×	`div-exp_binary64_1834`
6×	`div-inv_binary64_1780`
5×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
4×	`add-log-exp_binary64_1822` `cbrt-undiv_binary64_1817`
3×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
2×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `unswap-sqr_binary64_1751` `associate-r_binary64_1723` `*-commutative_binary64_1714`

Counts

4 → 193

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x))))))))
11.0ms	(/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x)))))))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 10862 to 6954 computations (36% saved)

series828.0ms (6.6%)

Error

Counts

4 → 15

Calls

4 calls:

399.0ms	(/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x)))))))
357.0ms	(/.f64 1 (/.f64 (sqrt.f64 PI.f64) (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 2 (.f64 2/3 (*.f64 x x))))))))
41.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1602 to 1205 computations (24.8% saved)

simplify180.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4943	12812
1	4943	12812

prune788.0ms (6.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	208	4	212

Error

Counts

212 → 4

Compiler

Compiled 10514 to 6674 computations (36.5% saved)

regimes1.3s (10.3%)

Accuracy

Total 0.2b remaining (99.8%)

Threshold costs 0.2b (99.8%)

Compiler

Compiled 24921 to 12343 computations (50.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	80
1	42	80

end0.0ms (0%)

sample3.9s (30.9%)

Algorithm

1×

intervals

Results

973.0ms	8000×	body	128	valid
124.0ms	8003×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 3996 to 2082 computations (47.9% saved)

Details

analyze11.0ms (0.1%)

sample72.0ms (0.6%)

simplify293.0ms (2.3%)

prune7.0ms (0.1%)

localize45.0ms (0.4%)

rewrite711.0ms (5.6%)

series518.0ms (4.1%)

simplify149.0ms (1.2%)

prune452.0ms (3.6%)

localize29.0ms (0.2%)

rewrite328.0ms (2.6%)

series625.0ms (5%)

simplify93.0ms (0.7%)

prune300.0ms (2.4%)

localize18.0ms (0.1%)

rewrite287.0ms (2.3%)

series566.0ms (4.5%)

simplify83.0ms (0.7%)

prune254.0ms (2%)

localize19.0ms (0.1%)

rewrite765.0ms (6.1%)

series828.0ms (6.6%)

simplify180.0ms (1.4%)

prune788.0ms (6.2%)

regimes1.3s (10.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (30.9%)

Profiling