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)

simplify382.0ms (14.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (285.0ms)

Iter	Nodes	Cost
0	7544	20

prune7.0ms (0.3%)

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: 0.0b

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

rewrite68.0ms (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:

23.0ms	(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)))

series139.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
40.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
28.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
22.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify103.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4855	2730
1	4855	2730

prune135.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0b

Counts

130 → 2

Compiler

Compiled 2607 to 1689 computations (35.2% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite170.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`*-un-lft-identity_binary64_760`
125×	`cbrt-prod_binary64_791`
91×	`times-frac_binary64_766`
72×	`add-sqr-sqrt_binary64_782`
64×	`distribute-lft-out_binary64_711`
52×	`div-inv_binary64_757`
43×	`add-cube-cbrt_binary64_795`
33×	`cbrt-div_binary64_792`
26×	`swap-sqr_binary64_727`
25×	`distribute-rgt-out_binary64_713`
21×	`sqrt-prod_binary64_776`
18×	`associate-r_binary64_700` `associate-l_binary64_701`
11×	`flip3-+_binary64_763` `frac-add_binary64_768` `flip-+_binary64_734` `pow1_binary64_821`
9×	`pow1/3_binary64_842` `frac-times_binary64_770`
7×	`distribute-rgt1-in_binary64_716`
6×	`add-exp-log_binary64_798`
4×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`associate-l/_binary64_703` `associate-r/_binary64_702`
2×	`pow-sqr_binary64_733` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `prod-exp_binary64_809` `pow-plus_binary64_823` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 177

Calls

4 calls:

63.0ms	(.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
25.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
23.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
23.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series290.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
71.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
69.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
68.0ms	(cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify129.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4863	6248
1	4863	6248

prune536.0ms (19.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	189	2	191

Merged error: 0b

Counts

191 → 2

Compiler

Compiled 9030 to 5888 computations (34.8% saved)

regimes42.0ms (1.6%)

Compiler: Compiled 304 to 220 computations (27.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	20
1	29	20

end0.0ms (0%)

sample649.0ms (24%)

Algorithm

1×

intervals

Results

422.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 111 to 82 computations (26.1% saved)

Details

analyze5.0ms (0.2%)

sample19.0ms (0.7%)

simplify382.0ms (14.1%)

prune7.0ms (0.3%)

localize9.0ms (0.3%)

rewrite68.0ms (2.5%)

series139.0ms (5.2%)

simplify103.0ms (3.8%)

prune135.0ms (5%)

localize14.0ms (0.5%)

rewrite170.0ms (6.3%)

series290.0ms (10.7%)

simplify129.0ms (4.8%)

prune536.0ms (19.9%)

regimes42.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample649.0ms (24%)

Profiling