Details

analyze55.0ms (1.5%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	3×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify238.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

prune7.0ms (0.2%)

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

0.3b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_11672`
22×	`add-exp-log_binary64_11710`
20×	`add-sqr-sqrt_binary64_11694`
16×	`add-cbrt-cube_binary64_11708`
15×	`associate-r_binary64_11612`
14×	`pow1_binary64_11733`
12×	`add-cube-cbrt_binary64_11707`
7×	`prod-exp_binary64_11721`
6×	`cancel-sign-sub-inv_binary64_11638` `add-log-exp_binary64_11711`
5×	`cbrt-unprod_binary64_11705` `distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622` `pow-prod-down_binary64_11743`
4×	`div-exp_binary64_11723` `sqrt-prod_binary64_11688` `distribute-lft-out_binary64_11623` `associate-l_binary64_11613`
3×	`distribute-lft-out--_binary64_11624` `times-frac_binary64_11678` `div-inv_binary64_11669` `associate-/l*_binary64_11617`
2×	`cbrt-undiv_binary64_11706` `1-exp_binary64_11716` `pow-flip_binary64_11746` `associate--l+_binary64_11609` `associate-r/_binary64_11614` `unswap-sqr_binary64_11640` `difference-of-squares_binary64_11641` `-commutative_binary64_11603` `rec-exp_binary64_11722` `sub-neg_binary64_11665`
1×	`inv-pow_binary64_11757` `clear-num_binary64_11671` `sum-log_binary64_11763` `difference-of-sqr-1_binary64_11642` `associate-/r*_binary64_11616` `flip-+_binary64_11646` `flip3-+_binary64_11675` `+-commutative_binary64_11602` `flip3--_binary64_11676` `frac-2neg_binary64_11683` `flip--_binary64_11647`

Counts

4 → 99

Calls

4 calls:

14.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms	(/.f64 1 (*.f64 x 9))

series84.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
17.0ms	(*.f64 3 (sqrt.f64 x))
16.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5251	1423

prune132.0ms (3.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Error

0.0b

Counts

113 → 12

Compiler

Compiled 2219 to 1616 computations (27.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1 x) 9))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
0.3b	(/.f64 (/.f64 1 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite60.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_11678`
60×	`add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
52×	`add-cube-cbrt_binary64_11707`
20×	`add-exp-log_binary64_11710`
16×	`add-cbrt-cube_binary64_11708`
14×	`associate-r_binary64_11612`
13×	`associate-/l*_binary64_11617`
11×	`pow1_binary64_11733`
6×	`div-exp_binary64_11723` `cancel-sign-sub-inv_binary64_11638` `add-log-exp_binary64_11711`
5×	`distribute-lft-in_binary64_11621` `div-inv_binary64_11669` `distribute-rgt-in_binary64_11622`
4×	`cbrt-unprod_binary64_11705` `sqrt-prod_binary64_11688` `prod-exp_binary64_11721` `pow-prod-down_binary64_11743` `associate-l_binary64_11613`
3×	`cbrt-undiv_binary64_11706` `associate-/r*_binary64_11616`
2×	`distribute-lft-out--_binary64_11624` `associate--l+_binary64_11609` `associate-r/_binary64_11614` `unswap-sqr_binary64_11640` `difference-of-squares_binary64_11641` `distribute-lft-out_binary64_11623` `-commutative_binary64_11603` `sub-neg_binary64_11665`
1×	`clear-num_binary64_11671` `1-exp_binary64_11716` `sum-log_binary64_11763` `difference-of-sqr-1_binary64_11642` `flip-+_binary64_11646` `flip3-+_binary64_11675` `+-commutative_binary64_11602` `flip3--_binary64_11676` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619` `flip--_binary64_11647` `rec-exp_binary64_11722`

Counts

4 → 141

Calls

4 calls:

22.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
13.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
7.0ms	(/.f64 (/.f64 1 x) 9)
5.0ms	(*.f64 3 (sqrt.f64 x))

series89.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
16.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
16.0ms	(/.f64 (/.f64 1 x) 9)
16.0ms	(*.f64 3 (sqrt.f64 x))

simplify87.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4918	2213
1	4918	2213

prune175.0ms (4.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	154	11	165

Error

0.0b

Counts

165 → 11

Compiler

Compiled 3199 to 2307 computations (27.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) 9)
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_11678`
59×	`add-sqr-sqrt_binary64_11694`
51×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
38×	`sqrt-prod_binary64_11688`
34×	`add-exp-log_binary64_11710`
25×	`associate-/l*_binary64_11617`
22×	`add-cbrt-cube_binary64_11708`
14×	`div-exp_binary64_11723`
10×	`pow1_binary64_11733`
9×	`associate-r_binary64_11612` `associate-l_binary64_11613`
7×	`cbrt-undiv_binary64_11706` `associate-/r*_binary64_11616`
6×	`prod-exp_binary64_11721`
4×	`cbrt-unprod_binary64_11705` `add-log-exp_binary64_11711` `unswap-sqr_binary64_11640` `div-inv_binary64_11669`
3×	`1-exp_binary64_11716` `pow-flip_binary64_11746` `rec-exp_binary64_11722`
2×	`clear-num_binary64_11671` `frac-2neg_binary64_11683` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743`
1×	`inv-pow_binary64_11757` `pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `associate-/l/_binary64_11619`

Counts

4 → 157

Calls

4 calls:

14.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))
5.0ms	(*.f64 (sqrt.f64 x) 9)
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(/.f64 1 (sqrt.f64 x))

series68.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 1 (sqrt.f64 x))
15.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))
15.0ms	(*.f64 3 (sqrt.f64 x))
14.0ms	(*.f64 (sqrt.f64 x) 9)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4910	2024
1	4910	2024

prune201.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	170	10	180

Error

0.0b

Counts

180 → 10

Compiler

Compiled 3971 to 2512 computations (36.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.2b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.4b	(/.f64 1/9 x)

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_11672`
20×	`add-sqr-sqrt_binary64_11694`
16×	`add-cube-cbrt_binary64_11707`
13×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
11×	`pow1_binary64_11733`
9×	`times-frac_binary64_11678` `associate-l_binary64_11613`
6×	`associate-r_binary64_11612` `add-log-exp_binary64_11711` `associate-*r/_binary64_11614`
5×	`distribute-lft-in_binary64_11621` `distribute-rgt-in_binary64_11622`
4×	`cbrt-unprod_binary64_11705` `sqrt-prod_binary64_11688` `prod-exp_binary64_11721` `distribute-lft-out_binary64_11623` `pow-prod-down_binary64_11743`
3×	`associate-/r_binary64_11616` `flip-+_binary64_11646` `flip3-+_binary64_11675` `associate-/l_binary64_11617`
2×	`unswap-sqr_binary64_11640` `*-commutative_binary64_11603`
1×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `clear-num_binary64_11671` `sum-log_binary64_11763` `+-commutative_binary64_11602` `frac-2neg_binary64_11683` `div-inv_binary64_11669`

Counts

4 → 91

Calls

4 calls:

13.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
13.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
7.0ms	(+.f64 (/.f64 1/9 x) y)
3.0ms	(/.f64 1/9 x)

series103.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
32.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
18.0ms	(+.f64 (/.f64 1/9 x) y)
14.0ms	(/.f64 1/9 x)

simplify76.0ms (2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4877	1561
1	4877	1561

prune92.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	103	10	113

Error

0.0b

Counts

113 → 10

Compiler

Compiled 1792 to 1219 computations (32% saved)

regimes278.0ms (7.5%)

Accuracy

Total 0.4b remaining (97.5%)

Threshold costs 0.4b (97.5%)

Compiler

Compiled 3053 to 2623 computations (14.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	17	25

end0.0ms (0%)

sample1.7s (44.7%)

Algorithm

1×

intervals

Results

350.0ms	8000×	body	128	valid
5.0ms	121×	body	128	nan
4.0ms	85×	body	128	invalid

Compiler

Compiled 1055 to 905 computations (14.2% saved)

Details

analyze55.0ms (1.5%)

sample18.0ms (0.5%)

simplify238.0ms (6.4%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite37.0ms (1%)

series84.0ms (2.3%)

simplify46.0ms (1.2%)

prune132.0ms (3.5%)

localize11.0ms (0.3%)

rewrite60.0ms (1.6%)

series89.0ms (2.4%)

simplify87.0ms (2.3%)

prune175.0ms (4.7%)

localize10.0ms (0.3%)

rewrite42.0ms (1.1%)

series68.0ms (1.8%)

simplify84.0ms (2.3%)

prune201.0ms (5.4%)

localize8.0ms (0.2%)

rewrite42.0ms (1.1%)

series103.0ms (2.8%)

simplify76.0ms (2%)

prune92.0ms (2.5%)

regimes278.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (44.7%)

Profiling