Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample30.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	98×	body	1024	valid
3.0ms	42×	body	512	valid
2.0ms	9×	body	2048	valid
2.0ms	86×	body	128	valid
1.0ms	21×	body	256	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify101.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9

prune2.0ms (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

42.0b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(-.f64 (exp.f64 x) 1)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
2.3b	(-.f64 (exp.f64 x) 1)

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1805`
30×	`*-un-lft-identity_binary64_1783`
21×	`times-frac_binary64_1789`
15×	`add-cube-cbrt_binary64_1818`
10×	`difference-of-squares_binary64_1752`
7×	`associate-/l*_binary64_1728`
5×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`div-sub_binary64_1788` `div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

2 → 64

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0ms	(-.f64 (exp.f64 x) 1)

series48.0ms (1.8%)

Counts

2 → 12

Calls

2 calls:

32.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
16.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 134 to 114 computations (14.9% saved)

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4961	1076
1	4961	1076

prune77.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	4	77

Error

Counts

77 → 4

Compiler

Compiled 941 to 520 computations (44.7% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 x 1/6)
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0b	(+.f64 1/2 (*.f64 x 1/6))
0.0b	(+.f64 1/2 (*.f64 x 1/6))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1805`
7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
6×	`associate-l_binary64_1724` `associate-r_binary64_1723`
5×	`add-log-exp_binary64_1822`
2×	`associate-r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
1×	`+-commutative_binary64_1713` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733` `sum-log_binary64_1874`

Counts

3 → 51

Calls

6 calls:

6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)
3.0ms	(+.f64 1/2 (*.f64 x 1/6))
0.0ms	(+.f64 1/2 (*.f64 x 1/6))
0.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))

series93.0ms (3.4%)

Counts

3 → 15

Calls

3 calls:

49.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
27.0ms	(+.f64 1/2 (*.f64 x 1/6))
17.0ms	(*.f64 x 1/6)

Compiler

Compiled 212 to 192 computations (9.4% saved)

simplify74.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4841	612
1	4841	612

prune50.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Error

Counts

70 → 4

Compiler

Compiled 865 to 678 computations (21.6% saved)

localize13.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))) x)
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))
0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
2.3b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite45.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1805`
62×	`*-un-lft-identity_binary64_1783`
48×	`times-frac_binary64_1789`
40×	`difference-of-squares_binary64_1752`
30×	`add-cube-cbrt_binary64_1818`
20×	`difference-of-sqr-1_binary64_1753`
18×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
16×	`sqr-pow_binary64_1755` `associate-/l*_binary64_1728`
8×	`add-log-exp_binary64_1822`
7×	`add-cbrt-cube_binary64_1819`
6×	`add-exp-log_binary64_1821`
5×	`distribute-lft-out--_binary64_1735` `pow1_binary64_1844`
4×	`pow-pow_binary64_1855`
3×	`pow-unpow_binary64_1860` `cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727` `exp-prod_binary64_1835`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `+-commutative_binary64_1713` `rem-cube-cbrt_binary64_1806` `cube-mult_binary64_1813` `distribute-lft-out_binary64_1734` `unpow3_binary64_1849` `div-inv_binary64_1780` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 149

Calls

8 calls:

13.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
4.0ms	(+.f64 (exp.f64 x) 1)
3.0ms	(pow.f64 (exp.f64 x) 3)
0.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))

series213.0ms (7.7%)

Counts

4 → 24

Calls

4 calls:

122.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
40.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
33.0ms	(pow.f64 (exp.f64 x) 3)
18.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 606 to 458 computations (24.4% saved)

simplify92.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5113	4573

prune261.0ms (9.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	173	4	177

Error

Counts

177 → 4

Compiler

Compiled 4688 to 3028 computations (35.4% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(cbrt.f64 (-.f64 (exp.f64 x) 1))
0.0b	(*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1)))
0.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1))) (cbrt.f64 (-.f64 (exp.f64 x) 1)))
0.0b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1))) (cbrt.f64 (-.f64 (exp.f64 x) 1))) x)
0.0b	(cbrt.f64 (-.f64 (exp.f64 x) 1))
2.3b	(-.f64 (exp.f64 x) 1)
2.3b	(-.f64 (exp.f64 x) 1)
2.3b	(-.f64 (exp.f64 x) 1)

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1805`
20×	`*-un-lft-identity_binary64_1783`
10×	`add-log-exp_binary64_1822`
9×	`cancel-sign-sub-inv_binary64_1749`
8×	`difference-of-squares_binary64_1752` `add-cube-cbrt_binary64_1818`
7×	`cbrt-prod_binary64_1814`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `flip--_binary64_1758` `pow1_binary64_1844`
3×	`diff-log_binary64_1875` `sub-neg_binary64_1776`
2×	`cbrt-div_binary64_1815`
1×	`pow1/3_binary64_1865`

Counts

4 → 71

Calls

8 calls:

5.0ms	(-.f64 (exp.f64 x) 1)
5.0ms	(-.f64 (exp.f64 x) 1)
5.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1))) (cbrt.f64 (-.f64 (exp.f64 x) 1))) x)

series153.0ms (5.5%)

Counts

4 → 22

Calls

4 calls:

87.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 1))
23.0ms	(-.f64 (exp.f64 x) 1)
21.0ms	(-.f64 (exp.f64 x) 1)
21.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 683 to 522 computations (23.6% saved)

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4807	949
1	4807	949

prune104.0ms (3.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	93	4	97

Error

Counts

97 → 4

Compiler

Compiled 2132 to 1370 computations (35.7% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	192
1	80	192

regimes67.0ms (2.4%)

Compiler: Compiled 291 to 239 computations (17.9% saved)

bsearch16.0ms (0.6%)

Steps

Iters	Range		Point
10	-0.050002429633695195	-3.100575507639719e-13	-0.00010875733412229075

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0.5%)

Accuracy

Total 0.3b remaining (87.7%)

Threshold costs 0.3b (87.7%)

Compiler

Compiled 44 to 38 computations (13.6% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 20 to 17 computations (15% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	29
1	24	29

end0.0ms (0%)

sample1.1s (38.6%)

Algorithm

1×

intervals

Results

412.0ms	2704×	body	1024	valid
117.0ms	1305×	body	512	valid
77.0ms	3051×	body	128	valid
50.0ms	264×	body	2048	valid
41.0ms	676×	body	256	valid

Compiler

Compiled 177 to 142 computations (19.8% saved)

Pareto

0.0

Details

analyze4.0ms (0.1%)

sample30.0ms (1.1%)

simplify101.0ms (3.6%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite20.0ms (0.7%)

series48.0ms (1.8%)

simplify64.0ms (2.3%)

prune77.0ms (2.8%)

localize6.0ms (0.2%)

rewrite16.0ms (0.6%)

series93.0ms (3.4%)

simplify74.0ms (2.7%)

prune50.0ms (1.8%)

localize13.0ms (0.5%)

rewrite45.0ms (1.6%)

series213.0ms (7.7%)

simplify92.0ms (3.3%)

prune261.0ms (9.4%)

localize9.0ms (0.3%)

rewrite26.0ms (0.9%)

series153.0ms (5.5%)

simplify86.0ms (3.1%)

prune104.0ms (3.8%)

simplify5.0ms (0.2%)

regimes67.0ms (2.4%)

bsearch16.0ms (0.6%)

regimes15.0ms (0.5%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (38.6%)

Profiling