Details

analyze9.0ms (0.3%)

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)

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify273.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5574	20

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

Merged error: 0.3b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite59.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_767`
26×	`times-frac_binary64_773`
21×	`add-sqr-sqrt_binary64_789`
16×	`distribute-lft-out_binary64_718`
15×	`log-prod_binary64_853`
13×	`add-cube-cbrt_binary64_802`
12×	`div-inv_binary64_764`
11×	`sqrt-prod_binary64_783`
6×	`distribute-rgt-out_binary64_720`
5×	`pow1_binary64_828` `add-log-exp_binary64_806`
4×	`add-exp-log_binary64_805`
3×	`log-div_binary64_854` `add-cbrt-cube_binary64_803`
2×	`frac-add_binary64_775` `flip-+_binary64_741` `distribute-rgt1-in_binary64_723` `flip3-+_binary64_770` `difference-of-squares_binary64_736` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `log-pow_binary64_856` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `rem-log-exp_binary64_808` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771`

Counts

3 → 68

Calls

3 calls:

25.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
24.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series222.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

111.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
59.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
52.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4936	1676
1	4936	1676

prune114.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	2	78

Merged error: 0b

Counts

78 → 2

Compiler

Compiled 2023 to 1370 computations (32.3% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
0.2b	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))

rewrite169.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_767`
134×	`times-frac_binary64_773`
127×	`sqrt-prod_binary64_783`
109×	`add-sqr-sqrt_binary64_789`
70×	`add-cube-cbrt_binary64_802`
42×	`distribute-lft-out_binary64_718`
32×	`log-prod_binary64_853`
26×	`associate-+r+_binary64_699`
16×	`div-inv_binary64_764`
14×	`difference-of-squares_binary64_736`
12×	`associate-/r*_binary64_711`
11×	`pow1_binary64_828` `associate-/l*_binary64_712`
10×	`add-exp-log_binary64_805`
8×	`distribute-rgt-out_binary64_720` `add-cbrt-cube_binary64_803`
7×	`add-log-exp_binary64_806`
6×	`associate-+l+_binary64_700` `distribute-neg-in_binary64_728`
5×	`log-pow_binary64_856`
4×	`distribute-rgt-neg-in_binary64_725`
3×	`log-div_binary64_854` `associate-+r-_binary64_701` `pow-flip_binary64_841` `flip-+_binary64_741` `sum-log_binary64_858` `flip3-+_binary64_770` `div-exp_binary64_818`
2×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `frac-add_binary64_775` `+-commutative_binary64_697` `distribute-rgt1-in_binary64_723` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`neg-sub0_binary64_762` `1-exp_binary64_811` `neg-log_binary64_860` `pow1/2_binary64_847` `rec-exp_binary64_817` `flip--_binary64_742` `sqrt-pow1_binary64_785` `sqrt-undiv_binary64_788` `flip3--_binary64_771` `inv-pow_binary64_852` `associate-+l-_binary64_702`

Counts

4 → 211

Calls

4 calls:

69.0ms	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
59.0ms	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))

series325.0ms (11%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
67.0ms	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
50.0ms	(/.f64 1 (sqrt.f64 x))
47.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))

simplify91.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5072	4961

prune290.0ms (9.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	223	2	225

Merged error: 0b

Counts

225 → 2

Compiler

Compiled 6110 to 3040 computations (50.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)
0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x))
0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x)))

rewrite137.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_767`
23×	`add-sqr-sqrt_binary64_789`
22×	`cbrt-prod_binary64_798`
20×	`sqrt-prod_binary64_783`
19×	`add-cube-cbrt_binary64_802`
16×	`cube-prod_binary64_795` `unpow-prod-down_binary64_846`
14×	`times-frac_binary64_773`
12×	`log-prod_binary64_853` `div-inv_binary64_764`
10×	`distribute-lft-out_binary64_718`
8×	`difference-of-squares_binary64_736`
7×	`pow1_binary64_828`
6×	`add-exp-log_binary64_805` `add-log-exp_binary64_806` `distribute-rgt-out_binary64_720`
5×	`add-cbrt-cube_binary64_803`
4×	`cube-div_binary64_796` `sqrt-div_binary64_784`
3×	`log-div_binary64_854` `pow-unpow_binary64_844` `pow-pow_binary64_839`
2×	`sqr-pow_binary64_739` `frac-add_binary64_775` `flip-+_binary64_741` `cube-mult_binary64_797` `cbrt-div_binary64_799` `distribute-rgt1-in_binary64_723` `flip3-+_binary64_770` `flip--_binary64_742` `unpow3_binary64_833` `flip3--_binary64_771`
1×	`pow-to-exp_binary64_836` `pow1/3_binary64_849` `pow-exp_binary64_835` `log-pow_binary64_856` `rem-cbrt-cube_binary64_791` `+-commutative_binary64_697` `sum-log_binary64_858` `rem-cube-cbrt_binary64_790` `pow1/2_binary64_847` `rem-log-exp_binary64_808` `sqrt-pow1_binary64_785` `sqrt-pow2_binary64_786`

Counts

4 → 116

Calls

4 calls:

57.0ms	(+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x))
53.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x)))
6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))
6.0ms	(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)

series280.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x)))
77.0ms	(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)
52.0ms	(+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x))
52.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))

simplify85.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4920	2484
1	4920	2484

prune145.0ms (4.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0b

Counts

130 → 2

Compiler

Compiled 2625 to 1795 computations (31.6% saved)

regimes9.0ms (0.3%)

Compiler: Compiled 38 to 29 computations (23.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms (0%)

sample625.0ms (21.1%)

Algorithm

1×

intervals

Results

431.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 69 to 52 computations (24.6% saved)

Details

analyze9.0ms (0.3%)

sample20.0ms (0.7%)

simplify273.0ms (9.2%)

prune2.0ms (0.1%)

localize12.0ms (0.4%)

rewrite59.0ms (2%)

series222.0ms (7.5%)

simplify66.0ms (2.2%)

prune114.0ms (3.9%)

localize14.0ms (0.5%)

rewrite169.0ms (5.7%)

series325.0ms (11%)

simplify91.0ms (3.1%)

prune290.0ms (9.8%)

localize13.0ms (0.5%)

rewrite137.0ms (4.6%)

series280.0ms (9.5%)

simplify85.0ms (2.9%)

prune145.0ms (4.9%)

regimes9.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample625.0ms (21.1%)

Profiling