Details

analyze84.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
37.5%	62.4%	0.1%	5
43.7%	56.2%	0.1%	6
71.8%	28.1%	0.1%	7
73.4%	25%	1.7%	8
80.4%	16.4%	3.2%	9
80.8%	14%	5.2%	10
84.1%	8.8%	7.1%	11
84.2%	7.4%	8.4%	12
85.8%	4.5%	9.7%	13
85.8%	3.8%	10.4%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample12.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify226.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	53	11
1	53	11

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`times-frac_binary64_3153` `*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
3×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-/r_binary64_3091` `associate-/l_binary64_3092`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `pow1_binary64_3208` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `add-log-exp_binary64_3186` `div-inv_binary64_3144`

Counts

1 → 27

Calls

1 calls:

3.0ms

(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

series74.0ms (2.6%)

Counts

1 → 3

Calls

1 calls:

74.0ms

(/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 y))

simplify54.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5110	540

prune44.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	4	31

Merged error: 0b

Counts

31 → 4

Compiler

Compiled 442 to 100 computations (77.4% saved)

localize13.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))
0.1b	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))

rewrite39.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_3153`
52×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
16×	`associate-/r*_binary64_3091`
15×	`add-exp-log_binary64_3185`
9×	`add-cbrt-cube_binary64_3183`
8×	`div-exp_binary64_3198`
6×	`associate-/l*_binary64_3092` `div-inv_binary64_3144`
4×	`cbrt-undiv_binary64_3181`
3×	`pow1_binary64_3208`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `add-log-exp_binary64_3186` `1-exp_binary64_3191` `rec-exp_binary64_3197`
1×	`inv-pow_binary64_3232` `pow-flip_binary64_3221` `associate-/r/_binary64_3093`

Counts

2 → 103

Calls

2 calls:

13.0ms	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
6.0ms	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))

series142.0ms (5%)

Counts

2 → 6

Calls

2 calls:

72.0ms	(/.f64 1 (/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y))))
70.0ms	(/.f64 (fabs.f64 y) (fabs.f64 (-.f64 x y)))

simplify98.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4970	2346
1	4970	2346

prune102.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	109	4	113

Merged error: 0b

Counts

113 → 4

Compiler

Compiled 1828 to 423 computations (76.9% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 x y)))
0.3b	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
0.3b	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))

rewrite34.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_3169`
40×	`times-frac_binary64_3153`
36×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
35×	`sqrt-prod_binary64_3163`
22×	`associate-r_binary64_3087`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`pow1_binary64_3208`
6×	`unswap-sqr_binary64_3115` `associate-/l_binary64_3092` `associate-l*_binary64_3088`
4×	`add-log-exp_binary64_3186`
3×	`associate-/r*_binary64_3091`
2×	`rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `div-inv_binary64_3144`
1×	`-commutative_binary64_3078` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `associate-r/_binary64_3089`

Counts

4 → 113

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
5.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))

series348.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y))
100.0ms	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (/.f64 (sqrt.f64 (fabs.f64 (-.f64 x y))) (fabs.f64 y)))
84.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
52.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))

simplify120.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5405	2278

prune105.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	4	129

Merged error: 0b

Counts

129 → 4

Compiler

Compiled 2449 to 303 computations (87.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (sqrt.f64 (fabs.f64 y)))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 (fabs.f64 y))) (/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y))))
0.4b	(/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y)))

rewrite51.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-sqr-sqrt_binary64_3169`
94×	`times-frac_binary64_3153`
65×	`*-un-lft-identity_binary64_3147`
59×	`add-cube-cbrt_binary64_3182`
53×	`sqrt-prod_binary64_3163`
31×	`add-exp-log_binary64_3185`
22×	`associate-r_binary64_3087` `associate-l_binary64_3088`
19×	`add-cbrt-cube_binary64_3183`
15×	`unswap-sqr_binary64_3115`
12×	`associate-/r*_binary64_3091`
11×	`div-exp_binary64_3198`
8×	`prod-exp_binary64_3196`
7×	`pow1_binary64_3208`
6×	`cbrt-undiv_binary64_3181` `associate-/l*_binary64_3092`
4×	`cbrt-unprod_binary64_3180` `div-inv_binary64_3144`
3×	`pow-flip_binary64_3221` `add-log-exp_binary64_3186` `1-exp_binary64_3191` `rec-exp_binary64_3197`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `inv-pow_binary64_3232` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `associate-*r/_binary64_3089`

Counts

3 → 167

Calls

3 calls:

22.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fabs.f64 y))) (/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y))))
5.0ms	(/.f64 1 (sqrt.f64 (fabs.f64 y)))
5.0ms	(/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y)))

series276.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y)))
86.0ms	(/.f64 1 (sqrt.f64 (fabs.f64 y)))
68.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fabs.f64 y))) (/.f64 (fabs.f64 (-.f64 x y)) (sqrt.f64 (fabs.f64 y))))

simplify101.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5088	3392

prune155.0ms (5.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 3429 to 784 computations (77.1% saved)

regimes72.0ms (2.5%)

Compiler: Compiled 579 to 320 computations (44.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	11
1	17	11

end0.0ms (0%)

sample677.0ms (23.6%)

Algorithm

1×

intervals

Results

238.0ms	8000×	body	128	valid
6.0ms	201×	body	128	invalid

Compiler

Compiled 202 to 115 computations (43.1% saved)

Details

analyze84.0ms (2.9%)

sample12.0ms (0.4%)

simplify226.0ms (7.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite5.0ms (0.2%)

series74.0ms (2.6%)

simplify54.0ms (1.9%)

prune44.0ms (1.5%)

localize13.0ms (0.5%)

rewrite39.0ms (1.4%)

series142.0ms (5%)

simplify98.0ms (3.4%)

prune102.0ms (3.5%)

localize14.0ms (0.5%)

rewrite34.0ms (1.2%)

series348.0ms (12.1%)

simplify120.0ms (4.2%)

prune105.0ms (3.7%)

localize8.0ms (0.3%)

rewrite51.0ms (1.8%)

series276.0ms (9.6%)

simplify101.0ms (3.5%)

prune155.0ms (5.4%)

regimes72.0ms (2.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample677.0ms (23.6%)

Profiling