Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample59.0ms (0.3%)

Algorithm

1×

intervals

Results

25.0ms	83×	body	1024	valid
9.0ms	120×	body	128	valid
8.0ms	34×	body	512	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

21.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

3.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite139.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_3423`
118×	`times-frac_binary64_3407`
117×	`*-un-lft-identity_binary64_3401`
76×	`sqrt-prod_binary64_3417`
56×	`add-cube-cbrt_binary64_3436`
27×	`cancel-sign-sub-inv_binary64_3367`
25×	`difference-of-squares_binary64_3370`
13×	`distribute-lft-out--_binary64_3353` `associate-/r*_binary64_3345`
12×	`add-exp-log_binary64_3439`
11×	`distribute-lft-out_binary64_3352`
9×	`pow1_binary64_3462`
8×	`add-cbrt-cube_binary64_3437`
7×	`div-inv_binary64_3398`
6×	`add-log-exp_binary64_3440` `sqrt-div_binary64_3418` `associate-/l*_binary64_3346` `pow-flip_binary64_3475`
4×	`associate-/r/_binary64_3347` `div-exp_binary64_3452`
3×	`flip-+_binary64_3375` `pow1/2_binary64_3481` `flip3-+_binary64_3404` `sqrt-pow1_binary64_3419`
2×	`cbrt-undiv_binary64_3435` `clear-num_binary64_3400` `inv-pow_binary64_3486` `rec-exp_binary64_3451` `1-exp_binary64_3445` `frac-2neg_binary64_3412`
1×	`flip--_binary64_3376` `diff-log_binary64_3493` `frac-sub_binary64_3410` `flip3--_binary64_3405` `rem-sqrt-square_binary64_3414` `sub-neg_binary64_3394`

Counts

4 → 189

Calls

8 calls:

76.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))

series118.0ms (0.6%)

Counts

4 → 14

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
29.0ms	(sqrt.f64 (+.f64 x 1))
19.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 324 to 283 computations (12.7% saved)

simplify164.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5145	3271

prune519.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	190	13	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	13	204

Error

20.3b

Counts

204 → 13

Compiler

Compiled 3600 to 2687 computations (25.4% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.5b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite104.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_3423`
42×	`sqrt-prod_binary64_3417`
38×	`*-un-lft-identity_binary64_3401`
13×	`add-cube-cbrt_binary64_3436`
12×	`difference-of-squares_binary64_3370`
11×	`add-exp-log_binary64_3439` `add-cbrt-cube_binary64_3437`
10×	`associate-/l*_binary64_3346` `times-frac_binary64_3407`
9×	`distribute-lft-out--_binary64_3353` `pow1_binary64_3462`
7×	`associate-r_binary64_3341`
6×	`add-log-exp_binary64_3440` `associate-l_binary64_3342` `sqrt-div_binary64_3418` `cancel-sign-sub-inv_binary64_3367`
5×	`distribute-lft-out_binary64_3352`
4×	`unswap-sqr_binary64_3369` `associate-*r/_binary64_3343`
3×	`pow-prod-down_binary64_3472` `flip-+_binary64_3375` `pow1/2_binary64_3481` `flip3-+_binary64_3404` `sqrt-pow1_binary64_3419`
2×	`cbrt-undiv_binary64_3435` `associate-/r/_binary64_3347` `flip--_binary64_3376` `cbrt-unprod_binary64_3434` `flip3--_binary64_3405` `prod-exp_binary64_3450` `div-exp_binary64_3452` `associate-/l/_binary64_3348`
1×	`clear-num_binary64_3400` `div-inv_binary64_3398` `diff-log_binary64_3493` `sqrt-unprod_binary64_3421` `rem-sqrt-square_binary64_3414` `associate-/r_binary64_3345` `sub-neg_binary64_3394` `div-sub_binary64_3406` `frac-2neg_binary64_3412` `-commutative_binary64_3332`

Counts

4 → 113

Calls

8 calls:

36.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
21.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
19.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series237.0ms (1.3%)

Counts

4 → 17

Calls

4 calls:

94.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
59.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
53.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
30.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 528 to 419 computations (20.6% saved)

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5205	2116

prune257.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	140	3	143

Error

0.3b

Counts

143 → 3

Compiler

Compiled 2557 to 1643 computations (35.7% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite136.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_3401`
78×	`times-frac_binary64_3407`
55×	`sqrt-prod_binary64_3417`
47×	`add-sqr-sqrt_binary64_3423`
45×	`distribute-lft-out_binary64_3352`
39×	`add-cube-cbrt_binary64_3436`
32×	`add-exp-log_binary64_3439`
27×	`associate-/l*_binary64_3346`
20×	`add-cbrt-cube_binary64_3437`
14×	`div-exp_binary64_3452`
9×	`pow1_binary64_3462`
8×	`associate-/r/_binary64_3347`
7×	`cbrt-undiv_binary64_3435` `associate-r_binary64_3341` `associate-/r*_binary64_3345`
6×	`add-log-exp_binary64_3440` `associate-l_binary64_3342` `flip-+_binary64_3375` `flip3-+_binary64_3404`
5×	`prod-exp_binary64_3450`
4×	`div-inv_binary64_3398` `unswap-sqr_binary64_3369` `sqrt-div_binary64_3418` `associate-*r/_binary64_3343`
3×	`cbrt-unprod_binary64_3434` `rec-exp_binary64_3451` `1-exp_binary64_3445` `pow-prod-down_binary64_3472`
2×	`clear-num_binary64_3400` `frac-2neg_binary64_3412` `pow1/2_binary64_3481` `sqrt-pow1_binary64_3419`
1×	`+-commutative_binary64_3331` `inv-pow_binary64_3486` `sqrt-unprod_binary64_3421` `sum-log_binary64_3492` `*-commutative_binary64_3332` `associate-/l/_binary64_3348` `pow-flip_binary64_3475`

Counts

4 → 166

Calls

8 calls:

44.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series213.0ms (1.1%)

Counts

4 → 15

Calls

4 calls:

96.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
35.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 386 to 331 computations (14.2% saved)

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune553.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Error

0.0b

Counts

184 → 10

Compiler

Compiled 4213 to 2914 computations (30.8% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.0b	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.0b	(+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite147.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64_3423`
82×	`times-frac_binary64_3407`
66×	`*-un-lft-identity_binary64_3401`
54×	`add-exp-log_binary64_3439`
53×	`add-cube-cbrt_binary64_3436`
38×	`sqrt-prod_binary64_3417`
29×	`associate-r_binary64_3341`
28×	`associate-l_binary64_3342`
22×	`add-cbrt-cube_binary64_3437`
20×	`div-exp_binary64_3452`
19×	`unswap-sqr_binary64_3369`
17×	`prod-exp_binary64_3450`
15×	`pow1_binary64_3462`
12×	`associate-/r/_binary64_3347`
11×	`flip-+_binary64_3375` `associate-*r/_binary64_3343` `flip3-+_binary64_3404`
10×	`rec-exp_binary64_3451` `associate-/r*_binary64_3345` `sqrt-div_binary64_3418` `1-exp_binary64_3445`
8×	`frac-add_binary64_3409`
7×	`distribute-rgt-out_binary64_3354`
6×	`cbrt-undiv_binary64_3435` `pow-prod-down_binary64_3472` `associate-/l*_binary64_3346` `pow-flip_binary64_3475`
5×	`cbrt-unprod_binary64_3434`
4×	`div-inv_binary64_3398` `inv-pow_binary64_3486` `add-log-exp_binary64_3440`
3×	`pow1/2_binary64_3481` `sqrt-pow1_binary64_3419`
2×	`clear-num_binary64_3400` `frac-2neg_binary64_3412` `*-commutative_binary64_3332`
1×	`un-div-inv_binary64_3399` `sqrt-unprod_binary64_3421` `distribute-lft-out_binary64_3352` `associate-*l/_binary64_3344` `frac-times_binary64_3411`

Counts

4 → 213

Calls

8 calls:

50.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
16.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
8.0ms	(/.f64 1 (sqrt.f64 x))
0.0ms	(sqrt.f64 (+.f64 x 1))

series205.0ms (1.1%)

Counts

4 → 18

Calls

4 calls:

76.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
54.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
48.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
26.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 468 to 399 computations (14.7% saved)

simplify207.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4925	5154
1	4925	5154

prune578.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	232	9	241

Error

0.0b

Counts

241 → 9

Compiler

Compiled 5723 to 3829 computations (33.1% saved)

simplify265.0ms (1.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (190.0ms)

Iter	Nodes	Cost
0	2462	2967
1	2462	2967

regimes327.0ms (1.8%)

Accuracy

Total 0.2b remaining (98.6%)

Threshold costs 0.2b (98.6%)

Compiler

Compiled 1867 to 1499 computations (19.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	17	26

end0.0ms (0%)

sample13.8s (74.2%)

Algorithm

1×

intervals

Results

632.0ms	2283×	body	1024	valid
301.0ms	4262×	body	128	valid
201.0ms	971×	body	512	valid
65.0ms	484×	body	256	valid

Compiler

Compiled 5656 to 4543 computations (19.7% saved)

Pareto

0.3871046088971962

Details

analyze3.0ms (0%)

sample59.0ms (0.3%)

simplify179.0ms (1%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite139.0ms (0.8%)

series118.0ms (0.6%)

simplify164.0ms (0.9%)

prune519.0ms (2.8%)

localize16.0ms (0.1%)

rewrite104.0ms (0.6%)

series237.0ms (1.3%)

simplify117.0ms (0.6%)

prune257.0ms (1.4%)

localize18.0ms (0.1%)

rewrite136.0ms (0.7%)

series213.0ms (1.1%)

simplify178.0ms (1%)

prune553.0ms (3%)

localize21.0ms (0.1%)

rewrite147.0ms (0.8%)

series205.0ms (1.1%)

simplify207.0ms (1.1%)

prune578.0ms (3.1%)

simplify265.0ms (1.4%)

regimes327.0ms (1.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample13.8s (74.2%)

Profiling