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)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify388.0ms (17.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (287.0ms)

Iter	Nodes	Cost
0	7544	20

prune3.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite37.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_2124`
37×	`times-frac_binary64_2130`
31×	`add-sqr-sqrt_binary64_2146`
24×	`add-cube-cbrt_binary64_2159`
23×	`sqrt-prod_binary64_2140`
15×	`log-prod_binary64_2210`
8×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `distribute-lft-out_binary64_2075`
7×	`div-inv_binary64_2121`
5×	`add-exp-log_binary64_2162`
4×	`add-cbrt-cube_binary64_2160`
3×	`pow1_binary64_2185` `associate-/r*_binary64_2068` `distribute-rgt-out_binary64_2077` `log-div_binary64_2211`
2×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `associate-/l/_binary64_2071`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `rem-log-exp_binary64_2165` `log-pow_binary64_2213` `distribute-rgt1-in_binary64_2080` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175` `frac-add_binary64_2132` `frac-2neg_binary64_2135`

Counts

2 → 76

Calls

4 calls:

23.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

series93.0ms (4.2%)

Counts

2 → 12

Calls

2 calls:

56.0ms	(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)

Compiler

Compiled 199 to 183 computations (8% saved)

simplify95.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4866	1877
1	4866	1877

prune103.0ms (4.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	1	89

Error

Counts

89 → 1

Compiler

Compiled 1719 to 1089 computations (36.6% saved)

localize12.0ms (0.5%)

Local error

Found 8 expressions with local error:

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

rewrite34.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
34×	`sqrt-prod_binary64_2140`
27×	`times-frac_binary64_2130`
25×	`add-cube-cbrt_binary64_2159`
10×	`difference-of-squares_binary64_2093` `sqrt-div_binary64_2141`
9×	`associate-/l*_binary64_2069`
7×	`pow1_binary64_2185` `log-div_binary64_2211` `add-exp-log_binary64_2162`
6×	`add-cbrt-cube_binary64_2160`
5×	`distribute-lft-out--_binary64_2076` `frac-add_binary64_2132`
4×	`add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`associate-/r*_binary64_2068` `log-prod_binary64_2210`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `associate-*l/_binary64_2067` `pow1/2_binary64_2204` `frac-times_binary64_2134` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `rem-log-exp_binary64_2165` `log-pow_binary64_2213` `distribute-lft-out_binary64_2075` `associate-*r/_binary64_2066` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 106

Calls

8 calls:

7.0ms	(log.f64 (+.f64 (/.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) x))))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) x)
4.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(log.f64 (+.f64 (/.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) x))))

series118.0ms (5.3%)

Counts

4 → 24

Calls

4 calls:

51.0ms	(log.f64 (+.f64 (/.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) x))))
27.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) x)
20.0ms	(sqrt.f64 (-.f64 1 x))
19.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 544 to 453 computations (16.7% saved)

simplify83.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5023	2212

prune155.0ms (6.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	130	1	131

Error

Counts

131 → 1

Compiler

Compiled 2842 to 2082 computations (26.7% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	149
1	92	149

regimes87.0ms (3.9%)

Compiler: Compiled 431 to 365 computations (15.3% saved)

bsearch0.0ms (0%)

regimes78.0ms (3.5%)

Compiler: Compiled 338 to 290 computations (14.2% saved)

bsearch0.0ms (0%)

regimes44.0ms (2%)

Compiler: Compiled 175 to 154 computations (12% saved)

bsearch0.0ms (0%)

regimes13.0ms (0.6%)

Compiler: Compiled 30 to 30 computations (0% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

Compiler: Compiled 13 to 15 computations (-15.4% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.3%)

Accuracy

Total 0.0b remaining (96.1%)

Threshold costs 0.0b (96.1%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch5.0ms (0.2%)

Compiler: Compiled 65 to 54 computations (16.9% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	99
1	69	99

end0.0ms (0%)

sample829.0ms (37.1%)

Algorithm

1×

intervals

Results

433.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 178 to 151 computations (15.2% saved)

Pareto

0.6547166242025217

Details

analyze5.0ms (0.2%)

sample21.0ms (0.9%)

simplify388.0ms (17.3%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite37.0ms (1.6%)

series93.0ms (4.2%)

simplify95.0ms (4.2%)

prune103.0ms (4.6%)

localize12.0ms (0.5%)

rewrite34.0ms (1.5%)

series118.0ms (5.3%)

simplify83.0ms (3.7%)

prune155.0ms (6.9%)

simplify5.0ms (0.2%)

regimes87.0ms (3.9%)

bsearch0.0ms (0%)

regimes78.0ms (3.5%)

bsearch0.0ms (0%)

regimes44.0ms (2%)

bsearch0.0ms (0%)

regimes13.0ms (0.6%)

bsearch0.0ms (0%)

regimes9.0ms (0.4%)

bsearch0.0ms (0%)

regimes7.0ms (0.3%)

bsearch5.0ms (0.2%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample829.0ms (37.1%)

Profiling