Details

analyze321.0ms (9.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	74×	body	1024	valid
4.0ms	45×	body	512	valid
2.0ms	104×	body	128	valid
2.0ms	12×	body	2048	valid
1.0ms	21×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify91.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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

40.3b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(-.f64 (exp.f64 x) 1)
0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.6b	(-.f64 (exp.f64 x) 1)

rewrite16.0ms (0.5%)

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-/r*_binary64_1727`
5×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `add-exp-log_binary64_1821` `cancel-sign-sub-inv_binary64_1749`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`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 → 63

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.0ms	(-.f64 (exp.f64 x) 1)

series60.0ms (1.8%)

Counts

2 → 12

Calls

2 calls:

43.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
17.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5105	1195

prune116.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

0.0b

Counts

76 → 3

Compiler

Compiled 1012 to 508 computations (49.8% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/12)
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.3b	(*.f64 x 1/12)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_1822`
6×	`add-sqr-sqrt_binary64_1805`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
3×	`associate-l_binary64_1724` `sum-log_binary64_1874` `associate-r_binary64_1723`
1×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `associate-+l+_binary64_1716` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

2 → 31

Calls

4 calls:

11.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
4.0ms	(*.f64 x 1/12)
0.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.0ms	(*.f64 x 1/12)

series59.0ms (1.7%)

Counts

2 → 12

Calls

2 calls:

41.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
17.0ms	(*.f64 x 1/12)

Compiler

Compiled 132 to 120 computations (9.1% saved)

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4926	453
1	4926	453

prune35.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

0.0b

Counts

46 → 3

Compiler

Compiled 539 to 429 computations (20.4% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.6b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
18×	`times-frac_binary64_1789`
14×	`add-cube-cbrt_binary64_1818`
10×	`difference-of-squares_binary64_1752`
6×	`add-exp-log_binary64_1821` `associate-/r*_binary64_1727`
5×	`distribute-lft-out--_binary64_1735`
4×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `cancel-sign-sub-inv_binary64_1749` `pow1_binary64_1844`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `div-exp_binary64_1834` `flip--_binary64_1758`
1×	`inv-pow_binary64_1868` `1-exp_binary64_1827` `div-inv_binary64_1780` `pow-flip_binary64_1857` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `sub-neg_binary64_1776` `rec-exp_binary64_1833`

Counts

2 → 62

Calls

4 calls:

7.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series58.0ms (1.7%)

Counts

2 → 12

Calls

2 calls:

39.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
20.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 140 to 131 computations (6.4% saved)

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune62.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

0.0b

Counts

77 → 3

Compiler

Compiled 931 to 597 computations (35.9% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
0.2b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 (exp.f64 x) 1)
0.2b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.3b	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
3.6b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite73.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_1789`
237×	`*-un-lft-identity_binary64_1783`
153×	`add-sqr-sqrt_binary64_1805`
109×	`add-cube-cbrt_binary64_1818`
88×	`difference-of-sqr--1_binary64_1754`
64×	`distribute-lft-out_binary64_1734`
42×	`associate-/r*_binary64_1727`
22×	`sqr-pow_binary64_1755` `unpow2_binary64_1848` `unpow-prod-down_binary64_1862`
11×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
9×	`add-exp-log_binary64_1821`
8×	`flip-+_binary64_1757` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
6×	`div-inv_binary64_1780`
4×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `pow1_binary64_1844`
2×	`associate-/l/_binary64_1730` `+-commutative_binary64_1713` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `clear-num_binary64_1782`

Counts

4 → 258

Calls

8 calls:

17.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
11.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(+.f64 (exp.f64 x) 1)
0.0ms	(+.f64 (exp.f64 x) 1)

series190.0ms (5.6%)

Counts

4 → 24

Calls

4 calls:

80.0ms	(/.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)))
60.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
30.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
20.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 456 to 347 computations (23.9% saved)

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5321	8221

prune350.0ms (10.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	282	3	285

Error

Counts

285 → 3

Compiler

Compiled 6587 to 3771 computations (42.8% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	192	518
1	192	518

regimes142.0ms (4.1%)

Compiler: Compiled 1261 to 905 computations (28.2% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.5%)

Compiler: Compiled 82 to 71 computations (13.4% saved)

bsearch0.0ms (0%)

regimes19.0ms (0.5%)

Compiler: Compiled 72 to 64 computations (11.1% saved)

bsearch0.0ms (0%)

regimes21.0ms (0.6%)

Compiler: Compiled 61 to 54 computations (11.5% saved)

bsearch15.0ms (0.4%)

Steps

Iters	Range		Point
8	-425944.2032468999	-249.9605996405551	-355.9775248099111

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.5%)

Compiler: Compiled 22 to 23 computations (-4.5% saved)

bsearch13.0ms (0.4%)

Steps

Iters	Range		Point
9	-249.9605996405551	-1.963308720893399e-06	-1.9853155584823636

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0.5%)

Compiler: Compiled 8 to 11 computations (-37.5% saved)

bsearch11.0ms (0.3%)

Steps

Iters	Range		Point
8	-425944.2032468999	-249.9605996405551	-355.9775248099111

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.2%)

Accuracy

Total 0.8b remaining (98.6%)

Threshold costs 0.8b (98.6%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 62 to 52 computations (16.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	89
1	41	89

end0.0ms (0%)

sample1.3s (37.7%)

Algorithm

1×

intervals

Results

380.0ms	2615×	body	1024	valid
103.0ms	1321×	body	512	valid
80.0ms	3133×	body	128	valid
49.0ms	293×	body	2048	valid
32.0ms	638×	body	256	valid
0.0ms	2×	body	2048	invalid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 405 to 302 computations (25.4% saved)

Pareto

0.9246590807028842

Details

analyze321.0ms (9.4%)

sample26.0ms (0.8%)

simplify91.0ms (2.7%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite16.0ms (0.5%)

series60.0ms (1.8%)

simplify65.0ms (1.9%)

prune116.0ms (3.4%)

localize6.0ms (0.2%)

rewrite17.0ms (0.5%)

series59.0ms (1.7%)

simplify61.0ms (1.8%)

prune35.0ms (1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.5%)

series58.0ms (1.7%)

simplify84.0ms (2.4%)

prune62.0ms (1.8%)

localize8.0ms (0.2%)

rewrite73.0ms (2.1%)

series190.0ms (5.6%)

simplify106.0ms (3.1%)

prune350.0ms (10.2%)

simplify10.0ms (0.3%)

regimes142.0ms (4.1%)

bsearch0.0ms (0%)

regimes18.0ms (0.5%)

bsearch0.0ms (0%)

regimes19.0ms (0.5%)

bsearch0.0ms (0%)

regimes21.0ms (0.6%)

bsearch15.0ms (0.4%)

regimes17.0ms (0.5%)

bsearch13.0ms (0.4%)

regimes15.0ms (0.5%)

bsearch11.0ms (0.3%)

regimes7.0ms (0.2%)

bsearch5.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (37.7%)

Profiling