Details

analyze172.0ms (1.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5512	47
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample68.0ms (0.7%)

Algorithm

1×

intervals

Results

53.0ms	256×	body	128	valid
3.0ms	259×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5512	47

prune8.0ms (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

2.3b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (*.f64 x x))

rewrite89.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_1789`
84×	`add-sqr-sqrt_binary64_1805`
79×	`*-un-lft-identity_binary64_1783`
70×	`add-cube-cbrt_binary64_1818` `associate-l_binary64_1724`
31×	`sqrt-prod_binary64_1799`
18×	`add-cbrt-cube_binary64_1819`
17×	`add-exp-log_binary64_1821`
7×	`pow1_binary64_1844`
6×	`add-log-exp_binary64_1822`
5×	`distribute-lft-out_binary64_1734` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `associate-r_binary64_1723`
4×	`associate-/l*_binary64_1728` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `unswap-sqr_binary64_1751`
3×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
2×	`associate-*r/_binary64_1725` `associate-/l/_binary64_1730` `frac-times_binary64_1793`
1×	`rem-exp-log_binary64_1823` `distribute-lft-in_binary64_1732` `pow1/2_binary64_1863` `associate-/r_binary64_1727` `exp-to-pow_binary64_1845` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796` `exp-prod_binary64_1835`

Counts

4 → 149

Calls

4 calls:

52.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series155.0ms (1.6%)

Counts

4 → 10

Calls

4 calls:

92.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
54.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify118.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4944	6254
1	4944	6254

prune365.0ms (3.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	137	22	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	22	161

Error

0.3b

Counts

161 → 22

Compiler

Compiled 7863 to 3663 computations (53.4% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
28×	`pow1_binary64_1844`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
19×	`cbrt-prod_binary64_1814` `pow1/3_binary64_1865`
18×	`sqrt-pow1_binary64_1801`
12×	`times-frac_binary64_1789`
11×	`pow-flip_binary64_1857`
10×	`add-exp-log_binary64_1821`
6×	`add-cbrt-cube_binary64_1819` `swap-sqr_binary64_1750` `pow-prod-up_binary64_1853` `associate-l_binary64_1724` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
5×	`sqrt-prod_binary64_1799`
4×	`associate-/r*_binary64_1727` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `pow-plus_binary64_1846` `pow2_binary64_1864`
2×	`pow1/2_binary64_1863` `div-exp_binary64_1834`
1×	`inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `1-exp_binary64_1827` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

4 → 115

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
7.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4984	1284
1	4984	1284

prune257.0ms (2.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	5	16	21
Picked	0	1	1
Done	0	0	0
Total	121	20	141

Error

0.3b

Counts

141 → 20

Compiler

Compiled 6129 to 3063 computations (50% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
0.7b	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
1.0b	(pow.f64 (exp.f64 x) x)
1.0b	(sqrt.f64 PI.f64)

rewrite108.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_1783`
18×	`add-sqr-sqrt_binary64_1805`
15×	`add-cube-cbrt_binary64_1818`
14×	`pow1_binary64_1844`
9×	`frac-add_binary64_1791` `flip-+_binary64_1757` `frac-times_binary64_1793` `flip3-+_binary64_1786`
8×	`distribute-lft-out_binary64_1734`
7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `unpow-prod-down_binary64_1862`
6×	`swap-sqr_binary64_1750` `pow-unpow_binary64_1860`
5×	`pow-pow_binary64_1855`
4×	`associate-l_binary64_1724` `add-log-exp_binary64_1822` `cube-prod_binary64_1811` `associate-r_binary64_1723`
3×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `sqrt-prod_binary64_1799` `cube-div_binary64_1812` `exp-prod_binary64_1835`
2×	`sqr-pow_binary64_1755` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`rem-cube-cbrt_binary64_1806` `distribute-lft-in_binary64_1732` `cube-mult_binary64_1813` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `unpow3_binary64_1849` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `pow1/2_binary64_1863` `pow-sqr_binary64_1756` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796` `pow2_binary64_1864`

Counts

4 → 108

Calls

4 calls:

51.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
23.0ms	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
3.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)

series90.0ms (1%)

Counts

4 → 10

Calls

4 calls:

35.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
34.0ms	(pow.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) 3)
22.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5128	3919

prune693.0ms (7.3%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	113	25	138

Error

0.2b

Counts

138 → 25

Compiler

Compiled 13094 to 7953 computations (39.3% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
1.0b	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
28×	`pow1_binary64_1844`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
19×	`cbrt-prod_binary64_1814` `pow1/3_binary64_1865`
18×	`sqrt-pow1_binary64_1801`
12×	`times-frac_binary64_1789`
11×	`pow-flip_binary64_1857`
10×	`add-exp-log_binary64_1821`
6×	`add-cbrt-cube_binary64_1819` `swap-sqr_binary64_1750` `pow-prod-up_binary64_1853` `associate-l_binary64_1724` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
5×	`sqrt-prod_binary64_1799`
4×	`associate-/r*_binary64_1727` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `pow-plus_binary64_1846` `pow2_binary64_1864`
2×	`pow1/2_binary64_1863` `div-exp_binary64_1834`
1×	`inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `1-exp_binary64_1827` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

4 → 115

Calls

4 calls:

7.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
7.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
4.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)))
0.0ms	(/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))))
0.0ms	(cbrt.f64 PI.f64)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4980	1353
1	4980	1353

prune208.0ms (2.2%)

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	20	22
Picked	0	1	1
Done	0	2	2
Total	119	25	144

Error

0.2b

Counts

144 → 25

Compiler

Compiled 5557 to 2347 computations (57.8% saved)

regimes1.0s (10.8%)

Accuracy

Total 1.1b remaining (84.9%)

Threshold costs 0b (0%)

Compiler

Compiled 16055 to 10563 computations (34.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	60
1	33	60

end0.0ms (0%)

sample5.6s (59.3%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
103.0ms	8114×	pre	128	true
23.0ms	114×	body	128	invalid

Compiler

Compiled 5424 to 3571 computations (34.2% saved)

Details

analyze172.0ms (1.8%)

sample68.0ms (0.7%)

simplify78.0ms (0.8%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

rewrite89.0ms (0.9%)

series155.0ms (1.6%)

simplify118.0ms (1.2%)

prune365.0ms (3.8%)

localize31.0ms (0.3%)

rewrite36.0ms (0.4%)

series0.0ms (0%)

simplify76.0ms (0.8%)

prune257.0ms (2.7%)

localize35.0ms (0.4%)

rewrite108.0ms (1.1%)

series90.0ms (1%)

simplify94.0ms (1%)

prune693.0ms (7.3%)

localize32.0ms (0.3%)

rewrite37.0ms (0.4%)

series0.0ms (0%)

simplify62.0ms (0.7%)

prune208.0ms (2.2%)

regimes1.0s (10.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (59.3%)

Profiling