Details

analyze65.0ms (3.1%)

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
12.5%	87.4%	0.1%	4
31.2%	68.7%	0.1%	5
43.7%	56.2%	0.1%	6
56.2%	40.6%	3.2%	7
64%	29.7%	6.3%	8
71%	20.3%	8.7%	9
75.3%	15.2%	9.5%	10
79%	10.1%	10.8%	11
81.3%	7.7%	11%	12
83.2%	5%	11.8%	13
84.4%	3.8%	11.8%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample12.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	255×	body	128	valid
0.0ms	1×	body	512	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify108.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	256	10
1	256	10

prune6.0ms (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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_7921` `add-sqr-sqrt_binary64_7943`
5×	`add-cube-cbrt_binary64_7956`
4×	`add-log-exp_binary64_7960` `add-cbrt-cube_binary64_7957` `associate-l_binary64_7862` `pow1_binary64_7982` `add-exp-log_binary64_7959`
3×	`associate-r_binary64_7861` `cancel-sign-sub-inv_binary64_7887`
2×	`associate-*l/_binary64_7864`
1×	`flip3--_binary64_7925` `diff-log_binary64_8013` `distribute-lft-out_binary64_7872` `unswap-sqr_binary64_7889` `prod-exp_binary64_7970` `sub-neg_binary64_7914` `cbrt-unprod_binary64_7954` `*-commutative_binary64_7852` `flip3-+_binary64_7924` `flip--_binary64_7896` `flip-+_binary64_7895` `pow-prod-down_binary64_7992`

Counts

2 → 35

Calls

2 calls:

7.0ms	(*.f64 (+.f64 x 1) y)
6.0ms	(-.f64 (*.f64 (+.f64 x 1) y) x)

series34.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(*.f64 (+.f64 x 1) y)
15.0ms	(-.f64 (*.f64 (+.f64 x 1) y) x)

simplify50.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4971	449
1	4971	449

prune41.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	5	42

Error

Counts

42 → 5

Compiler

Compiled 538 to 351 computations (34.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
0.2b	(cbrt.f64 (+.f64 x 1))
0.2b	(cbrt.f64 (+.f64 x 1))
0.2b	(cbrt.f64 (+.f64 x 1))

rewrite29.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_7952`
35×	`*-un-lft-identity_binary64_7921`
23×	`add-sqr-sqrt_binary64_7943`
18×	`cbrt-div_binary64_7953`
15×	`add-cube-cbrt_binary64_7956`
11×	`pow1_binary64_7982`
9×	`distribute-lft-out_binary64_7872` `pow1/3_binary64_8003` `flip3-+_binary64_7924` `flip-+_binary64_7895` `swap-sqr_binary64_7888`
7×	`associate-r_binary64_7861` `associate-l_binary64_7862`
6×	`add-exp-log_binary64_7959`
4×	`add-log-exp_binary64_7960` `frac-times_binary64_7931` `add-cbrt-cube_binary64_7957` `unswap-sqr_binary64_7889`
2×	`associate-r/_binary64_7863` `associate-l/_binary64_7864` `pow-prod-up_binary64_7991` `pow-sqr_binary64_7894` `pow-prod-down_binary64_7992`
1×	`pow2_binary64_8002` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `pow-plus_binary64_7984` `*-commutative_binary64_7852`

Counts

4 → 95

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))

series103.0ms (5%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt.f64 (+.f64 x 1))
27.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
26.0ms	(cbrt.f64 (+.f64 x 1))
23.0ms	(cbrt.f64 (+.f64 x 1))

simplify105.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4982	1446
1	4982	1446

prune131.0ms (6.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	107	5	112

Error

Counts

112 → 5

Compiler

Compiled 2494 to 1852 computations (25.7% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1)) x)
3.6b	(.f64 y (-.f64 (.f64 x x) 1))
8.5b	(/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1))

rewrite41.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_7943`
19×	`*-un-lft-identity_binary64_7921`
10×	`add-cube-cbrt_binary64_7956` `add-cbrt-cube_binary64_7957` `add-exp-log_binary64_7959`
9×	`cancel-sign-sub-inv_binary64_7887`
7×	`times-frac_binary64_7927` `difference-of-squares_binary64_7890` `associate-/r*_binary64_7865`
6×	`associate-r_binary64_7861`
5×	`add-log-exp_binary64_7960` `pow1_binary64_7982`
4×	`distribute-lft-in_binary64_7870` `flip3--_binary64_7925` `distribute-rgt-in_binary64_7871` `associate-*r/_binary64_7863` `flip--_binary64_7896`
3×	`distribute-lft-out--_binary64_7873` `difference-of-sqr-1_binary64_7891` `sub-neg_binary64_7914` `associate-l_binary64_7862`
2×	`prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `associate-/r/_binary64_7867` `div-exp_binary64_7972` `associate-/l/_binary64_7868` `cbrt-undiv_binary64_7955`
1×	`diff-log_binary64_8013` `clear-num_binary64_7920` `unswap-sqr_binary64_7889` `frac-2neg_binary64_7932` `-commutative_binary64_7852` `associate-/l_binary64_7866` `div-inv_binary64_7918` `pow-prod-down_binary64_7992`

Counts

3 → 80

Calls

3 calls:

14.0ms	(-.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1)) x)
13.0ms	(/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1))
8.0ms	(.f64 y (-.f64 (.f64 x x) 1))

series141.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1))
45.0ms	(-.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) 1)) (-.f64 x 1)) x)
37.0ms	(.f64 y (-.f64 (.f64 x x) 1))

simplify61.0ms (3%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4988	1220
1	4988	1220

prune72.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Error

Counts

94 → 5

Compiler

Compiled 1466 to 877 computations (40.2% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 x 1) y)
0.1b	(.f64 (.f64 (+.f64 x 1) y) (*.f64 (+.f64 x 1) y))
4.7b	(-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x))
27.0b	(/.f64 (-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x)) (+.f64 x (*.f64 (+.f64 x 1) y)))

rewrite64.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`pow1_binary64_7982`
20×	`add-cbrt-cube_binary64_7957` `add-exp-log_binary64_7959`
18×	`pow-prod-down_binary64_7992`
17×	`*-un-lft-identity_binary64_7921` `add-sqr-sqrt_binary64_7943`
16×	`associate-*l/_binary64_7864`
15×	`add-cube-cbrt_binary64_7956`
12×	`times-frac_binary64_7927`
9×	`prod-exp_binary64_7970` `cbrt-unprod_binary64_7954`
8×	`flip3-+_binary64_7924` `flip-+_binary64_7895`
6×	`add-log-exp_binary64_7960`
5×	`associate-l_binary64_7862` `difference-of-squares_binary64_7890`
4×	`associate-r_binary64_7861` `frac-times_binary64_7931` `associate-/l*_binary64_7866` `pow-prod-up_binary64_7991` `pow-sqr_binary64_7894`
3×	`associate-/r*_binary64_7865`
2×	`flip3--_binary64_7925` `associate-r/_binary64_7863` `pow-plus_binary64_7984` `associate-/r/_binary64_7867` `-commutative_binary64_7852` `associate-/l/_binary64_7868` `flip--_binary64_7896`
1×	`div-sub_binary64_7926` `diff-log_binary64_8013` `clear-num_binary64_7920` `distribute-lft-out_binary64_7872` `pow2_binary64_8002` `unswap-sqr_binary64_7889` `cancel-sign-sub-inv_binary64_7887` `frac-2neg_binary64_7932` `sub-neg_binary64_7914` `div-exp_binary64_7972` `cbrt-undiv_binary64_7955` `div-inv_binary64_7918` `swap-sqr_binary64_7888`

Counts

4 → 112

Calls

4 calls:

18.0ms	(-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x))
17.0ms	(/.f64 (-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x)) (+.f64 x (*.f64 (+.f64 x 1) y)))
12.0ms	(.f64 (.f64 (+.f64 x 1) y) (*.f64 (+.f64 x 1) y))
6.0ms	(*.f64 (+.f64 x 1) y)

series147.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 (-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x)) (+.f64 x (*.f64 (+.f64 x 1) y)))
43.0ms	(-.f64 (.f64 (.f64 (+.f64 x 1) y) (.f64 (+.f64 x 1) y)) (.f64 x x))
24.0ms	(.f64 (.f64 (+.f64 x 1) y) (*.f64 (+.f64 x 1) y))
20.0ms	(*.f64 (+.f64 x 1) y)

simplify72.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5978	2367

prune144.0ms (7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	124	5	129

Error

Counts

129 → 5

Compiler

Compiled 3264 to 1966 computations (39.8% saved)

regimes66.0ms (3.2%)

Accuracy

Total 0.0b remaining (74.5%)

Threshold costs 0.0b (74.5%)

Compiler

Compiled 492 to 392 computations (20.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms (0%)

sample517.0ms (25.1%)

Algorithm

1×

intervals

Results

190.0ms	7999×	body	128	valid
2.0ms	84×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 173 to 139 computations (19.7% saved)

Details

analyze65.0ms (3.1%)

sample12.0ms (0.6%)

simplify108.0ms (5.3%)

prune6.0ms (0.3%)

localize5.0ms (0.2%)

rewrite15.0ms (0.7%)

series34.0ms (1.6%)

simplify50.0ms (2.4%)

prune41.0ms (2%)

localize8.0ms (0.4%)

rewrite29.0ms (1.4%)

series103.0ms (5%)

simplify105.0ms (5.1%)

prune131.0ms (6.4%)

localize8.0ms (0.4%)

rewrite41.0ms (2%)

series141.0ms (6.9%)

simplify61.0ms (3%)

prune72.0ms (3.5%)

localize9.0ms (0.4%)

rewrite64.0ms (3.1%)

series147.0ms (7.1%)

simplify72.0ms (3.5%)

prune144.0ms (7%)

regimes66.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample517.0ms (25.1%)

Profiling