Details

analyze100.0ms (3.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample15.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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

0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite98.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`*-un-lft-identity_binary64_3147`
26×	`add-sqr-sqrt_binary64_3169`
21×	`distribute-lft-out_binary64_3098`
18×	`times-frac_binary64_3153`
15×	`add-cube-cbrt_binary64_3182`
14×	`sqrt-prod_binary64_3163`
6×	`associate-/r*_binary64_3091`
5×	`add-exp-log_binary64_3185` `add-log-exp_binary64_3186` `add-cbrt-cube_binary64_3183`
4×	`pow1_binary64_3208`
3×	`flip3-+_binary64_3150` `flip-+_binary64_3121` `associate-/l*_binary64_3092`
2×	`associate-/r/_binary64_3093` `sqrt-div_binary64_3164`
1×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `sum-log_binary64_3238` `+-commutative_binary64_3077` `pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160`

Counts

3 → 71

Calls

3 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 1133 to 876 computations (22.7% saved)

series83.0ms (2.8%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

36.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 446 to 364 computations (18.4% saved)

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4923	1202
1	4923	1202

prune80.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Error

Counts

90 → 5

Compiler

Compiled 1172 to 885 computations (24.5% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite176.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

70×	`*-un-lft-identity_binary64_3147`
51×	`add-sqr-sqrt_binary64_3169`
38×	`times-frac_binary64_3153`
33×	`distribute-lft-out_binary64_3098`
27×	`add-cube-cbrt_binary64_3182`
24×	`associate-r_binary64_3087`
20×	`sqrt-prod_binary64_3163`
17×	`add-exp-log_binary64_3185`
11×	`add-cbrt-cube_binary64_3183`
8×	`pow1_binary64_3208`
6×	`add-log-exp_binary64_3186` `associate-/r*_binary64_3091`
4×	`div-exp_binary64_3198` `prod-exp_binary64_3196` `flip3-+_binary64_3150` `associate-/r/_binary64_3093` `flip-+_binary64_3121`
3×	`unswap-sqr_binary64_3115` `associate-l_binary64_3088` `associate-/l*_binary64_3092`
2×	`1-exp_binary64_3191` `rec-exp_binary64_3197` `cbrt-unprod_binary64_3180` `cbrt-undiv_binary64_3181` `div-inv_binary64_3144` `sqrt-div_binary64_3164`
1×	`pow-prod-down_binary64_3218` `un-div-inv_binary64_3145` `associate-r/_binary64_3089` `-commutative_binary64_3078` `inv-pow_binary64_3232` `pow-flip_binary64_3221` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `sum-log_binary64_3238` `+-commutative_binary64_3077` `pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160`

Counts

4 → 122

Calls

4 calls:

16.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
11.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 2243 to 1893 computations (15.6% saved)

series113.0ms (3.8%)

Error

Counts

4 → 24

Calls

4 calls:

34.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
28.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 672 to 558 computations (17% saved)

simplify92.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4842	1871
1	4842	1871

prune128.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Error

Counts

151 → 5

Compiler

Compiled 2130 to 1752 computations (17.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))

rewrite60.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`add-sqr-sqrt_binary64_3169`
6×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-cube-cbrt_binary64_3182` `-un-lft-identity_binary64_3147` `associate-l_binary64_3088` `associate-r*_binary64_3087`
4×	`associate-*r/_binary64_3089`
2×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `add-log-exp_binary64_3186` `cbrt-unprod_binary64_3180` `unswap-sqr_binary64_3115` `distribute-rgt-in_binary64_3097` `distribute-lft-in_binary64_3096` `flip3-+_binary64_3150` `flip-+_binary64_3121` `*-commutative_binary64_3078`

Counts

2 → 44

Calls

2 calls:

7.0ms	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))

Compiler

Compiled 876 to 655 computations (25.2% saved)

series84.0ms (2.8%)

Error

Counts

2 → 11

Calls

2 calls:

43.0ms	(.f64 x (+.f64 (.f64 x 1/16) -1/8))
34.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 (*.f64 x 1/16) -1/8))))

Compiler

Compiled 278 to 234 computations (15.8% saved)

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4962	799
1	4962	799

prune48.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	55	5	60

Error

Counts

60 → 5

Compiler

Compiled 908 to 675 computations (25.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite236.0ms (7.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

119×	`*-un-lft-identity_binary64_3147`
92×	`add-sqr-sqrt_binary64_3169`
79×	`sqrt-prod_binary64_3163`
76×	`times-frac_binary64_3153`
57×	`distribute-lft-out_binary64_3098`
47×	`add-cube-cbrt_binary64_3182`
42×	`associate-r_binary64_3087`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
7×	`pow1_binary64_3208`
6×	`add-log-exp_binary64_3186` `unswap-sqr_binary64_3115` `associate-l_binary64_3088` `associate-/l_binary64_3092` `associate-/r_binary64_3091`
4×	`flip3-+_binary64_3150` `associate-/r/_binary64_3093` `flip-+_binary64_3121`
2×	`div-exp_binary64_3198` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `cbrt-undiv_binary64_3181` `div-inv_binary64_3144` `sqrt-div_binary64_3164`
1×	`pow-prod-down_binary64_3218` `associate-r/_binary64_3089` `-commutative_binary64_3078` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `sum-log_binary64_3238` `+-commutative_binary64_3077` `pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160`

Counts

4 → 160

Calls

4 calls:

24.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3521 to 2199 computations (37.5% saved)

series130.0ms (4.4%)

Error

Counts

4 → 21

Calls

4 calls:

43.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
38.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
19.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 740 to 546 computations (26.2% saved)

simplify86.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5028	3000

prune159.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	181	5	186

Error

Counts

186 → 5

Compiler

Compiled 3197 to 1999 computations (37.5% saved)

regimes115.0ms (3.9%)

Accuracy

Total 0.2b remaining (99.8%)

Threshold costs 0.2b (99.8%)

Compiler

Compiled 1018 to 833 computations (18.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	12	15

end0.0ms (0%)

sample1.0s (33.7%)

Algorithm

1×

intervals

Results

223.0ms	7996×	body	128	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 464 to 380 computations (18.1% saved)

Details

analyze100.0ms (3.3%)

sample15.0ms (0.5%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite98.0ms (3.3%)

series83.0ms (2.8%)

simplify64.0ms (2.1%)

prune80.0ms (2.7%)

localize6.0ms (0.2%)

rewrite176.0ms (5.9%)

series113.0ms (3.8%)

simplify92.0ms (3.1%)

prune128.0ms (4.3%)

localize7.0ms (0.2%)

rewrite60.0ms (2%)

series84.0ms (2.8%)

simplify66.0ms (2.2%)

prune48.0ms (1.6%)

localize10.0ms (0.3%)

rewrite236.0ms (7.9%)

series130.0ms (4.4%)

simplify86.0ms (2.9%)

prune159.0ms (5.3%)

regimes115.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (33.7%)

Profiling