Details

analyze6.0ms (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)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify215.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

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)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite162.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

24×	`add-sqr-sqrt_binary64_1805`
19×	`add-exp-log_binary64_1821`
15×	`associate-r_binary64_1723`
13×	`add-cbrt-cube_binary64_1819`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow1_binary64_1844`
9×	`prod-exp_binary64_1832` `associate-l_binary64_1724`
8×	`unpow-prod-down_binary64_1862`
7×	`unswap-sqr_binary64_1751`
5×	`cbrt-unprod_binary64_1816`
4×	`add-log-exp_binary64_1822` `sqr-pow_binary64_1755`
3×	`sqrt-prod_binary64_1799` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
6.0ms	(*.f64 1/21 (pow.f64 x 6))
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2594 to 1766 computations (31.9% saved)

series126.0ms (1.9%)

Error

0.1b

Counts

4 → 9

Calls

4 calls:

45.0ms	(*.f64 1/21 (pow.f64 x 6))
39.0ms	(*.f64 1/5 (pow.f64 x 4))
31.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 702 to 566 computations (19.4% saved)

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5031	773

prune133.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

0.1b

Counts

93 → 3

Compiler

Compiled 2781 to 1868 computations (32.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite135.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-sqr-sqrt_binary64_1805`
14×	`add-exp-log_binary64_1821`
11×	`pow1_binary64_1844` `add-cbrt-cube_binary64_1819`
10×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`associate-r_binary64_1723`
6×	`sqrt-prod_binary64_1799` `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×	`pow-prod-down_binary64_1854`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `*-commutative_binary64_1714` `sqr-pow_binary64_1755`
1×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 70

Calls

4 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2525 to 1486 computations (41.1% saved)

series78.0ms (1.1%)

Error

0.1b

Counts

4 → 6

Calls

4 calls:

38.0ms	(*.f64 1/5 (pow.f64 x 4))
31.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 558 to 409 computations (26.7% saved)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4836	603
1	4836	603

prune121.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	76	3	79

Error

0.1b

Counts

79 → 3

Compiler

Compiled 2674 to 1556 computations (41.8% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

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)))))
0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (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)))
1.0b	(sqrt.f64 PI.f64)

rewrite657.0ms (9.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

119×	`add-exp-log_binary64_1821`
76×	`prod-exp_binary64_1832`
75×	`add-cbrt-cube_binary64_1819`
48×	`associate-l_binary64_1724`
46×	`add-sqr-sqrt_binary64_1805`
44×	`cbrt-unprod_binary64_1816`
40×	`times-frac_binary64_1789`
36×	`pow1_binary64_1844`
35×	`*-un-lft-identity_binary64_1783`
33×	`add-cube-cbrt_binary64_1818`
22×	`pow-prod-down_binary64_1854`
15×	`div-exp_binary64_1834` `associate-*l/_binary64_1726`
14×	`sqrt-prod_binary64_1799`
12×	`frac-add_binary64_1791`
9×	`cbrt-undiv_binary64_1817`
6×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `flip3-+_binary64_1786` `frac-times_binary64_1793` `flip-+_binary64_1757` `associate-*r/_binary64_1725`
5×	`associate-r_binary64_1723` `unswap-sqr_binary64_1751`
4×	`add-log-exp_binary64_1822`
3×	`div-inv_binary64_1780` `*-commutative_binary64_1714`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`

Counts

4 → 169

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)))))
29.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 15657 to 5315 computations (66.1% saved)

series448.0ms (6.6%)

Error

0.1b

Counts

4 → 9

Calls

4 calls:

295.0ms	(.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 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
62.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1323 to 724 computations (45.3% saved)

simplify130.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4910	5228
1	4910	5228

prune473.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	177	4	181

Error

Counts

181 → 4

Compiler

Compiled 10984 to 4937 computations (55.1% saved)

localize18.0ms (0.3%)

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)

rewrite222.0ms (3.3%)

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))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4117 to 2554 computations (38% saved)

series453.0ms (6.7%)

Error

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.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))
72.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
29.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1040 to 799 computations (23.2% saved)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4996	3574
1	4996	3574

prune205.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	111	3	114

Error

Counts

114 → 3

Compiler

Compiled 4187 to 2613 computations (37.6% saved)

regimes697.0ms (10.3%)

Accuracy

Total 0.1b remaining (99.7%)

Threshold costs 0.1b (99.7%)

Compiler

Compiled 16106 to 7483 computations (53.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample2.2s (31.8%)

Algorithm

1×

intervals

Results

736.0ms	8000×	body	128	valid
97.0ms	8003×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 2426 to 1183 computations (51.2% saved)

Details

analyze6.0ms (0.1%)

sample42.0ms (0.6%)

simplify215.0ms (3.2%)

prune7.0ms (0.1%)

localize22.0ms (0.3%)

rewrite162.0ms (2.4%)

series126.0ms (1.9%)

simplify54.0ms (0.8%)

prune133.0ms (2%)

localize21.0ms (0.3%)

rewrite135.0ms (2%)

series78.0ms (1.1%)

simplify90.0ms (1.3%)

prune121.0ms (1.8%)

localize27.0ms (0.4%)

rewrite657.0ms (9.7%)

series448.0ms (6.6%)

simplify130.0ms (1.9%)

prune473.0ms (7%)

localize18.0ms (0.3%)

rewrite222.0ms (3.3%)

series453.0ms (6.7%)

simplify80.0ms (1.2%)

prune205.0ms (3%)

regimes697.0ms (10.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (31.8%)

Profiling