Details

analyze359.0ms (8.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2142	26
1	2142	26
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify226.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	2142	13
1	2142	13

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_18151`
40×	`add-sqr-sqrt_binary64_18173`
30×	`times-frac_binary64_18157`
19×	`distribute-lft-out--_binary64_18103`
14×	`add-cube-cbrt_binary64_18186`
13×	`difference-of-squares_binary64_18120`
6×	`distribute-lft-out_binary64_18102` `associate-/r*_binary64_18095`
5×	`associate-/l*_binary64_18096`
3×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
2×	`flip3--_binary64_18155` `associate-/l/_binary64_18098` `flip--_binary64_18126` `associate-/r/_binary64_18097`
1×	`div-exp_binary64_18202` `div-inv_binary64_18148` `pow1_binary64_18212` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `div-sub_binary64_18156` `add-log-exp_binary64_18190` `cbrt-undiv_binary64_18185`

Counts

1 → 58

Calls

1 calls:

12.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series31.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

31.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5165	1357

prune52.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Error

Counts

62 → 5

Compiler

Compiled 1132 to 476 computations (58% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 2 (+.f64 x y)))
0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64_18151`
47×	`add-sqr-sqrt_binary64_18173`
38×	`times-frac_binary64_18157`
24×	`associate-r_binary64_18091` `add-cube-cbrt_binary64_18186`
15×	`distribute-lft-out--_binary64_18103` `add-exp-log_binary64_18189`
9×	`add-cbrt-cube_binary64_18187`
8×	`difference-of-squares_binary64_18120`
7×	`distribute-lft-out_binary64_18102`
6×	`associate-/r*_binary64_18095`
5×	`pow1_binary64_18212` `associate-l_binary64_18092`
4×	`div-exp_binary64_18202` `flip3--_binary64_18155` `flip--_binary64_18126` `associate-/r/_binary64_18097` `prod-exp_binary64_18200`
3×	`associate-/l*_binary64_18096` `unswap-sqr_binary64_18119`
2×	`1-exp_binary64_18195` `div-inv_binary64_18148` `associate-*l/_binary64_18094` `rec-exp_binary64_18201` `frac-times_binary64_18161` `add-log-exp_binary64_18190` `cbrt-unprod_binary64_18184` `cbrt-undiv_binary64_18185`
1×	`inv-pow_binary64_18236` `associate-r/_binary64_18093` `pow-flip_binary64_18225` `pow-prod-down_binary64_18222` `-commutative_binary64_18082` `un-div-inv_binary64_18149` `clear-num_binary64_18150` `frac-2neg_binary64_18162`

Counts

2 → 98

Calls

2 calls:

22.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
8.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

series53.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
22.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5257	1620

prune86.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	104	5	109

Error

Counts

109 → 5

Compiler

Compiled 1800 to 941 computations (47.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
0.6b	(cbrt.f64 (-.f64 x y))
0.6b	(cbrt.f64 (-.f64 x y))
0.6b	(cbrt.f64 (-.f64 x y))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod_binary64_18182`
37×	`add-sqr-sqrt_binary64_18173`
35×	`*-un-lft-identity_binary64_18151`
18×	`cbrt-div_binary64_18183`
15×	`add-cube-cbrt_binary64_18186`
11×	`pow1_binary64_18212`
10×	`swap-sqr_binary64_18118`
9×	`flip3--_binary64_18155` `pow1/3_binary64_18233` `distribute-lft-out--_binary64_18103` `flip--_binary64_18126`
8×	`associate-r_binary64_18091` `associate-l_binary64_18092`
7×	`difference-of-squares_binary64_18120`
6×	`add-exp-log_binary64_18189`
4×	`unswap-sqr_binary64_18119` `add-cbrt-cube_binary64_18187` `frac-times_binary64_18161` `add-log-exp_binary64_18190`
2×	`pow-sqr_binary64_18124` `associate-r/_binary64_18093` `associate-l/_binary64_18094` `pow-prod-down_binary64_18222` `pow-prod-up_binary64_18221`
1×	`pow-plus_binary64_18214` `pow2_binary64_18232` `*-commutative_binary64_18082` `prod-exp_binary64_18200` `cbrt-unprod_binary64_18184`

Counts

4 → 101

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
4.0ms	(cbrt.f64 (-.f64 x y))
3.0ms	(cbrt.f64 (-.f64 x y))
3.0ms	(cbrt.f64 (-.f64 x y))

series450.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt.f64 (-.f64 x y))
123.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
103.0ms	(cbrt.f64 (-.f64 x y))
101.0ms	(cbrt.f64 (-.f64 x y))

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4914	1626
1	4914	1626

prune104.0ms (2.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	113	5	118

Error

Counts

118 → 5

Compiler

Compiled 2898 to 914 computations (68.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.0b	(sqrt.f64 (-.f64 2 (+.f64 x y)))
0.1b	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))) (sqrt.f64 (-.f64 2 (+.f64 x y))))
0.3b	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))

rewrite184.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

1082×	`*-un-lft-identity_binary64_18151`
954×	`times-frac_binary64_18157`
754×	`add-sqr-sqrt_binary64_18173`
660×	`sqrt-prod_binary64_18167`
332×	`add-cube-cbrt_binary64_18186`
320×	`distribute-lft-out--_binary64_18103`
210×	`difference-of-squares_binary64_18120`
110×	`distribute-lft-out_binary64_18102`
56×	`associate-/l*_binary64_18096`
28×	`sqrt-div_binary64_18168`
24×	`associate-/r/_binary64_18097`
18×	`associate-/r*_binary64_18095`
15×	`flip3--_binary64_18155` `flip--_binary64_18126`
12×	`div-inv_binary64_18148`
11×	`add-cbrt-cube_binary64_18187` `add-exp-log_binary64_18189`
6×	`pow1_binary64_18212`
4×	`div-exp_binary64_18202` `add-log-exp_binary64_18190` `cbrt-undiv_binary64_18185`
3×	`associate-/l/_binary64_18098` `div-sub_binary64_18156`
2×	`rem-sqrt-square_binary64_18164` `sqrt-pow1_binary64_18169` `clear-num_binary64_18150` `frac-2neg_binary64_18162` `pow1/2_binary64_18231`

Counts

4 → 649

Calls

4 calls:

40.0ms	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))) (sqrt.f64 (-.f64 2 (+.f64 x y))))
13.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))
6.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))
6.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))

series157.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y))))
33.0ms	(/.f64 (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 2 (+.f64 x y)))) (sqrt.f64 (-.f64 2 (+.f64 x y))))
26.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))
23.0ms	(sqrt.f64 (-.f64 2 (+.f64 x y)))

simplify274.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

661 → 661

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5024	25890

prune1.2s (29.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	661	0	661
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	661	5	666

Error

Counts

666 → 5

Compiler

Compiled 19046 to 9271 computations (51.3% saved)

regimes49.0ms (1.2%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Compiler

Compiled 445 to 289 computations (35.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	13
1	37	13

end0.0ms (0%)

sample541.0ms (13%)

Algorithm

1×

intervals

Results

221.0ms	7999×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 175 to 116 computations (33.7% saved)

Details

analyze359.0ms (8.6%)

sample17.0ms (0.4%)

simplify226.0ms (5.4%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

rewrite17.0ms (0.4%)

series31.0ms (0.8%)

simplify63.0ms (1.5%)

prune52.0ms (1.2%)

localize7.0ms (0.2%)

rewrite38.0ms (0.9%)

series53.0ms (1.3%)

simplify74.0ms (1.8%)

prune86.0ms (2.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.8%)

series450.0ms (10.8%)

simplify92.0ms (2.2%)

prune104.0ms (2.5%)

localize8.0ms (0.2%)

rewrite184.0ms (4.4%)

series157.0ms (3.8%)

simplify274.0ms (6.6%)

prune1.2s (29.5%)

regimes49.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample541.0ms (13%)

Profiling