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)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify269.0ms (8.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

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)))

rewrite57.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_751`
26×	`times-frac_binary64_757`
21×	`add-sqr-sqrt_binary64_772`
16×	`distribute-lft-out_binary64_704`
15×	`log-prod_binary64_834`
13×	`add-cube-cbrt_binary64_783`
12×	`div-inv_binary64_748`
11×	`sqrt-prod_binary64_766`
6×	`distribute-rgt-out_binary64_706`
5×	`pow1_binary64_809` `add-log-exp_binary64_787`
4×	`add-exp-log_binary64_786`
3×	`log-div_binary64_835` `add-cbrt-cube_binary64_784`
2×	`flip3-+_binary64_754` `distribute-rgt1-in_binary64_709` `sqrt-div_binary64_767` `frac-add_binary64_759` `flip-+_binary64_725` `difference-of-squares_binary64_720`
1×	`+-commutative_binary64_683` `rem-log-exp_binary64_789` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `flip--_binary64_726` `log-pow_binary64_837` `sum-log_binary64_839` `sqrt-pow1_binary64_768` `flip3--_binary64_755`

Counts

3 → 68

Calls

3 calls:

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

series201.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

104.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
55.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
42.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5033	1676

prune86.0ms (2.7%)

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 1512 to 991 computations (34.5% saved)

localize14.0ms (0.4%)

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))

rewrite171.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_751`
134×	`times-frac_binary64_757`
127×	`sqrt-prod_binary64_766`
109×	`add-sqr-sqrt_binary64_772`
70×	`add-cube-cbrt_binary64_783`
42×	`distribute-lft-out_binary64_704`
32×	`log-prod_binary64_834`
26×	`associate-+r+_binary64_685`
16×	`div-inv_binary64_748`
14×	`difference-of-squares_binary64_720`
12×	`associate-/r*_binary64_697`
11×	`pow1_binary64_809` `associate-/l*_binary64_698`
10×	`add-exp-log_binary64_786`
8×	`add-cbrt-cube_binary64_784` `distribute-rgt-out_binary64_706`
7×	`add-log-exp_binary64_787`
6×	`associate-+l+_binary64_686` `distribute-neg-in_binary64_714`
5×	`log-pow_binary64_837`
4×	`distribute-rgt-neg-in_binary64_711`
3×	`log-div_binary64_835` `flip3-+_binary64_754` `associate-+r-_binary64_687` `sum-log_binary64_839` `flip-+_binary64_725` `pow-flip_binary64_822` `div-exp_binary64_799`
2×	`+-commutative_binary64_683` `associate-/l/_binary64_700` `distribute-rgt1-in_binary64_709` `sqrt-div_binary64_767` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `frac-add_binary64_759`
1×	`1-exp_binary64_792` `associate-+l-_binary64_688` `rec-exp_binary64_798` `pow1/2_binary64_828` `flip--_binary64_726` `inv-pow_binary64_833` `sqrt-undiv_binary64_771` `neg-log_binary64_841` `sqrt-pow1_binary64_768` `neg-sub0_binary64_746` `flip3--_binary64_755`

Counts

4 → 211

Calls

4 calls:

68.0ms	(+.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)))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
5.0ms	(/.f64 1 (sqrt.f64 x))

series318.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(+.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)))))
63.0ms	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
51.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
49.0ms	(/.f64 1 (sqrt.f64 x))

simplify148.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4872	4961
1	4872	4961

prune301.0ms (9.4%)

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 6055 to 2999 computations (50.5% saved)

localize11.0ms (0.4%)

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 (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_751`
23×	`add-sqr-sqrt_binary64_772`
22×	`cbrt-prod_binary64_779`
20×	`sqrt-prod_binary64_766`
19×	`add-cube-cbrt_binary64_783`
16×	`unpow-prod-down_binary64_827` `cube-prod_binary64_776`
14×	`times-frac_binary64_757`
12×	`log-prod_binary64_834` `div-inv_binary64_748`
10×	`distribute-lft-out_binary64_704`
8×	`difference-of-squares_binary64_720`
7×	`pow1_binary64_809`
6×	`add-log-exp_binary64_787` `add-exp-log_binary64_786` `distribute-rgt-out_binary64_706`
5×	`add-cbrt-cube_binary64_784`
4×	`cube-div_binary64_777` `sqrt-div_binary64_767`
3×	`log-div_binary64_835` `pow-pow_binary64_820` `pow-unpow_binary64_825`
2×	`cube-mult_binary64_778` `flip3-+_binary64_754` `distribute-rgt1-in_binary64_709` `sqr-pow_binary64_723` `flip--_binary64_726` `unpow3_binary64_814` `cbrt-div_binary64_780` `frac-add_binary64_759` `flip3--_binary64_755` `flip-+_binary64_725`
1×	`rem-cbrt-cube_binary64_774` `pow1/3_binary64_830` `pow-to-exp_binary64_817` `+-commutative_binary64_683` `rem-log-exp_binary64_789` `pow-exp_binary64_816` `pow1/2_binary64_828` `rem-cube-cbrt_binary64_773` `log-pow_binary64_837` `sum-log_binary64_839` `sqrt-pow1_binary64_768` `sqrt-pow2_binary64_769`

Counts

4 → 116

Calls

4 calls:

58.0ms	(+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x))
57.0ms	(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)

series290.0ms (9%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x)))
76.0ms	(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)
63.0ms	(+.f64 (/.f64 1 x) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3)) x))
42.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 3))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5011	2484

prune145.0ms (4.5%)

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 2574 to 1756 computations (31.8% saved)

regimes91.0ms (2.8%)

Compiler: Compiled 792 to 591 computations (25.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms (0%)

sample799.0ms (24.9%)

Algorithm

1×

intervals

Results

445.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 238 to 178 computations (25.2% saved)

Details

analyze5.0ms (0.2%)

sample20.0ms (0.6%)

simplify269.0ms (8.4%)

prune2.0ms (0.1%)

localize12.0ms (0.4%)

rewrite57.0ms (1.8%)

series201.0ms (6.2%)

simplify66.0ms (2.1%)

prune86.0ms (2.7%)

localize14.0ms (0.4%)

rewrite171.0ms (5.3%)

series318.0ms (9.9%)

simplify148.0ms (4.6%)

prune301.0ms (9.4%)

localize11.0ms (0.4%)

rewrite137.0ms (4.3%)

series290.0ms (9%)

simplify66.0ms (2.1%)

prune145.0ms (4.5%)

regimes91.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample799.0ms (24.9%)

Profiling