Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample19.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify384.0ms (13.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (285.0ms)

Iter	Nodes	Cost
0	7544	20

prune7.0ms (0.2%)

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

0.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite70.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_760`
50×	`times-frac_binary64_766`
43×	`add-sqr-sqrt_binary64_782`
31×	`sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795`
16×	`distribute-lft-out_binary64_711`
15×	`log-prod_binary64_846`
13×	`div-inv_binary64_757`
10×	`difference-of-squares_binary64_729`
8×	`associate-/l*_binary64_705`
7×	`add-exp-log_binary64_798`
6×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `distribute-rgt-out_binary64_713` `pow1_binary64_821`
4×	`sqrt-div_binary64_777`
3×	`log-div_binary64_847` `associate-/r*_binary64_704`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `distribute-rgt1-in_binary64_716` `frac-add_binary64_768` `flip-+_binary64_734` `flip--_binary64_735` `flip3--_binary64_764`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `log-pow_binary64_849` `+-commutative_binary64_690` `sum-log_binary64_851` `rem-log-exp_binary64_801` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 117

Calls

4 calls:

24.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
23.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series138.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
38.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
27.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
23.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify105.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4855	2730
1	4855	2730

prune137.0ms (4.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Error

Counts

130 → 2

Compiler

Compiled 2600 to 1691 computations (35% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
0.0b	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite41.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_782`
23×	`add-exp-log_binary64_798`
21×	`*-un-lft-identity_binary64_760`
13×	`add-cube-cbrt_binary64_795` `associate-r_binary64_700`
11×	`times-frac_binary64_766`
10×	`pow1_binary64_821`
9×	`add-cbrt-cube_binary64_796`
8×	`prod-exp_binary64_809`
7×	`sqrt-prod_binary64_776`
6×	`log-div_binary64_847` `add-log-exp_binary64_799`
5×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701` `rem-log-exp_binary64_801`
4×	`associate-*l/_binary64_703` `distribute-lft-out_binary64_711` `frac-times_binary64_770` `div-exp_binary64_811`
3×	`unswap-sqr_binary64_728`
2×	`difference-of-squares_binary64_729` `sqrt-div_binary64_777` `log-pow_binary64_849` `associate-*r/_binary64_702` `rec-exp_binary64_810` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `1-exp_binary64_804`
1×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `*-commutative_binary64_691` `flip--_binary64_735` `log-prod_binary64_846` `flip3--_binary64_764`

Counts

4 → 93

Calls

4 calls:

16.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
10.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
6.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series109.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
25.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))
21.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
16.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify98.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4863	1863
1	4863	1863

prune105.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	105	2	107

Error

Counts

107 → 2

Compiler

Compiled 1909 to 1341 computations (29.8% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (neg.f64 (.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)) (/.f64 1 (cbrt.f64 x)))))
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)

rewrite81.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_760`
34×	`log-prod_binary64_846`
28×	`cbrt-prod_binary64_791`
26×	`times-frac_binary64_766` `add-sqr-sqrt_binary64_782`
22×	`associate-+r+_binary64_692`
20×	`add-cube-cbrt_binary64_795`
16×	`distribute-lft-out_binary64_711`
12×	`associate-+l+_binary64_693` `distribute-neg-in_binary64_721`
7×	`div-inv_binary64_757`
6×	`sqrt-prod_binary64_776` `distribute-lft-in_binary64_709` `add-log-exp_binary64_799` `distribute-rgt-in_binary64_710`
5×	`pow1_binary64_821`
4×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `distribute-rgt-out_binary64_713`
3×	`pow1/3_binary64_842` `log-div_binary64_847` `associate-+r-_binary64_694`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `sum-log_binary64_851`
1×	`frac-add_binary64_768` `neg-sub0_binary64_755` `log-pow_binary64_849` `neg-log_binary64_853` `+-commutative_binary64_690` `associate-+l-_binary64_695` `distribute-lft1-in_binary64_715`

Counts

4 → 85

Calls

4 calls:

68.0ms	(+.f64 (neg.f64 (.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)) (/.f64 1 (cbrt.f64 x)))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series458.0ms (16.3%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(+.f64 (neg.f64 (.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (+.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 x)) (/.f64 1 (cbrt.f64 x)))))
87.0ms	(cbrt.f64 x)
84.0ms	(cbrt.f64 x)
84.0ms	(cbrt.f64 x)

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4887	1772
1	4887	1772

prune118.0ms (4.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	2	99

Error

Counts

99 → 2

Compiler

Compiled 2612 to 1501 computations (42.5% saved)

regimes66.0ms (2.4%)

Accuracy

Total 0.1b remaining (99.3%)

Threshold costs 0.1b (99.3%)

Compiler

Compiled 556 to 427 computations (23.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms (0%)

sample738.0ms (26.3%)

Algorithm

1×

intervals

Results

421.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 195 to 152 computations (22.1% saved)

Details

analyze5.0ms (0.2%)

sample19.0ms (0.7%)

simplify384.0ms (13.7%)

prune7.0ms (0.2%)

localize9.0ms (0.3%)

rewrite70.0ms (2.5%)

series138.0ms (4.9%)

simplify105.0ms (3.7%)

prune137.0ms (4.9%)

localize9.0ms (0.3%)

rewrite41.0ms (1.5%)

series109.0ms (3.9%)

simplify98.0ms (3.5%)

prune105.0ms (3.7%)

localize19.0ms (0.7%)

rewrite81.0ms (2.9%)

series458.0ms (16.3%)

simplify86.0ms (3.1%)

prune118.0ms (4.2%)

regimes66.0ms (2.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample738.0ms (26.3%)

Profiling