Details

analyze834.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample110.0ms (0.1%)

Algorithm

1×

intervals

Results

52.0ms	82×	body	1024	valid
22.0ms	40×	body	2048	valid
12.0ms	33×	body	512	valid
6.0ms	77×	body	128	valid
4.0ms	5×	body	4096	valid
4.0ms	19×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify273.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune4.0ms (0%)

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

Merged error: 53.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize29.0ms (0%)

Local error

Found 3 expressions with local error:

0.7b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
17.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite88.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_1783`
6×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822` `pow1_binary64_1844`
4×	`log-prod_binary64_1869` `add-exp-log_binary64_1821`
3×	`add-cbrt-cube_binary64_1819` `flip-+_binary64_1757` `sqrt-prod_binary64_1799` `flip3-+_binary64_1786`
2×	`distribute-lft-out_binary64_1734` `sqrt-div_binary64_1800` `log-div_binary64_1870`
1×	`log-pow_binary64_1872` `+-commutative_binary64_1713` `pow1/2_binary64_1863` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rem-log-exp_binary64_1824`

Counts

3 → 42

Calls

3 calls:

30.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
21.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
21.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

series313.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

139.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
108.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
66.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify217.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	5224	862

prune790.0ms (1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	23	28	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	29	52

Merged error: 0b

Counts

52 → 29

Compiler

Compiled 1259 to 874 computations (30.6% saved)

localize20.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
22.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1805`
15×	`associate-l_binary64_1724`
13×	`add-exp-log_binary64_1821`
10×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
8×	`unpow-prod-down_binary64_1862` `add-log-exp_binary64_1822`
7×	`add-cbrt-cube_binary64_1819` `unswap-sqr_binary64_1751`
6×	`prod-exp_binary64_1832`
4×	`sqr-pow_binary64_1755` `cube-prod_binary64_1811`
3×	`pow1_binary64_1844`
2×	`cbrt-unprod_binary64_1816` `diff-log_binary64_1875` `*-commutative_binary64_1714` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`flip3--_binary64_1787` `cube-mult_binary64_1813` `unpow3_binary64_1849` `cancel-sign-sub-inv_binary64_1749` `sum-log_binary64_1874` `associate--l+_binary64_1720` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

3 → 70

Calls

3 calls:

14.0ms	(*.f64 (pow.f64 x 3) 1/6)
13.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
12.0ms	(*.f64 3/40 (pow.f64 x 5))

series206.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(*.f64 3/40 (pow.f64 x 5))
57.0ms	(*.f64 (pow.f64 x 3) 1/6)
56.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify334.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (239.0ms)

Iter	Nodes	Cost
0	5018	1015

prune1.1s (1.4%)

Pruning

45 alts after pruning (43 fresh and 2 done)

	Pruned	Kept	Total
New	61	18	79
Fresh	2	25	27
Picked	0	1	1
Done	0	1	1
Total	63	45	108

Merged error: 0b

Counts

108 → 45

Compiler

Compiled 2305 to 1801 computations (21.9% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
22.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 1/6)))

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1805` `cbrt-prod_binary64_1814`
14×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
11×	`pow1_binary64_1844`
9×	`add-log-exp_binary64_1822`
8×	`pow1/3_binary64_1865`
6×	`swap-sqr_binary64_1750` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`add-cbrt-cube_binary64_1819` `unswap-sqr_binary64_1751`
2×	`pow-prod-up_binary64_1853` `diff-log_binary64_1875` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`flip3--_binary64_1787` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `cancel-sign-sub-inv_binary64_1749` `*-commutative_binary64_1714` `sum-log_binary64_1874` `associate--l+_binary64_1720` `flip--_binary64_1758` `sub-neg_binary64_1776` `pow2_binary64_1864`

Counts

4 → 76

Calls

4 calls:

35.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 1/6)))
29.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
5.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series1.2s (1.6%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(cbrt.f64 x)
349.0ms	(cbrt.f64 x)
317.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
161.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 1/6)))

simplify153.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4887	938
1	4887	938

prune2.2s (2.8%)

Pruning

52 alts after pruning (49 fresh and 3 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	5	37	42
Picked	0	1	1
Done	0	2	2
Total	81	52	133

Merged error: 0b

Counts

133 → 52

Compiler

Compiled 2947 to 2062 computations (30% saved)

localize32.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
0.6b	(pow.f64 (cbrt.f64 x) 5)
22.4b	(-.f64 (+.f64 x (.f64 (.f64 3/40 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)) (pow.f64 (cbrt.f64 x) 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `cbrt-prod_binary64_1814` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
6×	`unpow-prod-down_binary64_1862`
5×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
4×	`add-cbrt-cube_binary64_1819`
3×	`pow-unpow_binary64_1860` `pow1/3_binary64_1865`
2×	`diff-log_binary64_1875` `pow-pow_binary64_1855`
1×	`flip3--_binary64_1787` `sqr-pow_binary64_1755` `cancel-sign-sub-inv_binary64_1749` `sum-log_binary64_1874` `associate--l+_binary64_1720` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 57

Calls

4 calls:

14.0ms	(-.f64 (+.f64 x (.f64 (.f64 3/40 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)) (pow.f64 (cbrt.f64 x) 5))) (.f64 (pow.f64 x 3) 1/6))
5.0ms	(pow.f64 (cbrt.f64 x) 5)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series1.2s (1.5%)

Counts

4 → 12

Calls

4 calls:

404.0ms	(pow.f64 (cbrt.f64 x) 5)
313.0ms	(cbrt.f64 x)
250.0ms	(cbrt.f64 x)
195.0ms	(-.f64 (+.f64 x (.f64 (.f64 3/40 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)) (pow.f64 (cbrt.f64 x) 5))) (.f64 (pow.f64 x 3) 1/6))

simplify141.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4853	955
1	4853	955

prune1.5s (1.9%)

Pruning

70 alts after pruning (66 fresh and 4 done)

	Pruned	Kept	Total
New	47	22	69
Fresh	4	44	48
Picked	0	1	1
Done	0	3	3
Total	51	70	121

Merged error: 0b

Counts

121 → 70

Compiler

Compiled 1792 to 1183 computations (34% saved)

regimes4.6s (5.8%)

Compiler: Compiled 13975 to 10908 computations (21.9% saved)

bsearch40.1s (51.4%)

Steps

Iters	Range		Point
10	4.612153234730046e-14	107134.2559352631	0.9609921084103406
8	-1.0702121956382065	-6.891705645522554e-05	-1.042983533250168

Compiler

Compiled 1 to 1 computations (0% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	99	91
1	99	91

end0.0ms (0%)

sample22.3s (28.6%)

Algorithm

1×

intervals

Results

1.7s	2502×	body	1024	valid
798.0ms	1229×	body	2048	valid
480.0ms	1227×	body	512	valid
207.0ms	2373×	body	128	valid
134.0ms	619×	body	256	valid
48.0ms	50×	body	4096	valid

Compiler

Compiled 5240 to 4043 computations (22.8% saved)

Pareto

0.3297624469222738

Details

analyze834.0ms (1.1%)

sample110.0ms (0.1%)

simplify273.0ms (0.4%)

prune4.0ms (0%)

localize29.0ms (0%)

rewrite88.0ms (0.1%)

series313.0ms (0.4%)

simplify217.0ms (0.3%)

prune790.0ms (1%)

localize20.0ms (0%)

rewrite51.0ms (0.1%)

series206.0ms (0.3%)

simplify334.0ms (0.4%)

prune1.1s (1.4%)

localize57.0ms (0.1%)

rewrite98.0ms (0.1%)

series1.2s (1.6%)

simplify153.0ms (0.2%)

prune2.2s (2.8%)

localize32.0ms (0%)

rewrite33.0ms (0%)

series1.2s (1.5%)

simplify141.0ms (0.2%)

prune1.5s (1.9%)

regimes4.6s (5.8%)

bsearch40.1s (51.4%)

simplify50.0ms (0.1%)

end0.0ms (0%)

sample22.3s (28.6%)

Profiling