Details

analyze66.0ms (1.9%)

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
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample31.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	233×	body	128	valid
4.0ms	10×	body	1024	valid
2.0ms	9×	body	512	valid
1.0ms	4×	body	256	valid
0.0ms	4×	body	128	invalid
0.0ms	2×	body	128	overflowed

Compiler

Compiled 19 to 19 computations (0% saved)

simplify225.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4811	14
1	4811	14

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: 0.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_3488`
8×	`log-prod_binary64_3574`
6×	`add-log-exp_binary64_3527`
5×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523`
4×	`add-exp-log_binary64_3526` `log-div_binary64_3575` `associate--l+_binary64_3425` `pow1_binary64_3549`
3×	`distribute-lft-out_binary64_3439` `add-cbrt-cube_binary64_3524` `flip-+_binary64_3462` `flip3-+_binary64_3491`
2×	`associate--l-_binary64_3426`
1×	`rem-log-exp_binary64_3529` `log-pow_binary64_3577` `flip3--_binary64_3492` `diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `+-commutative_binary64_3418` `flip--_binary64_3463` `sum-log_binary64_3579` `sub-neg_binary64_3481`

Counts

3 → 45

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series98.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
43.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
7.0ms	(+.f64 1 (exp.f64 x))

simplify105.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4858	767
1	4858	767

prune52.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0.0b

Counts

55 → 3

Compiler

Compiled 823 to 470 computations (42.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
0.7b	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_3488`
14×	`cbrt-prod_binary64_3519`
11×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523`
10×	`pow1_binary64_3549`
8×	`unpow-prod-down_binary64_3567` `cube-prod_binary64_3516`
6×	`add-exp-log_binary64_3526` `add-log-exp_binary64_3527`
5×	`log-pow_binary64_3577` `add-cbrt-cube_binary64_3524`
4×	`log-prod_binary64_3574`
3×	`pow-unpow_binary64_3565`
2×	`unpow3_binary64_3554` `distribute-lft-out_binary64_3439` `flip-+_binary64_3462` `flip3-+_binary64_3491` `log-div_binary64_3575` `sqr-pow_binary64_3460` `cube-mult_binary64_3518`
1×	`pow-exp_binary64_3556` `rem-log-exp_binary64_3529` `rem-cube-cbrt_binary64_3511` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `rem-cbrt-cube_binary64_3512` `sum-log_binary64_3579` `pow1/3_binary64_3570` `pow-pow_binary64_3560`

Counts

4 → 75

Calls

4 calls:

4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
2.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))

series182.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
45.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
42.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
7.0ms	(+.f64 1 (exp.f64 x))

simplify96.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4885	1105
1	4885	1105

prune84.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

Compiler

Compiled 1402 to 894 computations (36.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (*.f64 x y)))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`log-prod_binary64_3574`
26×	`*-un-lft-identity_binary64_3488`
20×	`sqrt-prod_binary64_3504`
14×	`add-sqr-sqrt_binary64_3510`
13×	`add-cube-cbrt_binary64_3523`
10×	`pow1_binary64_3549`
9×	`associate-+r+_binary64_3420`
8×	`sqrt-div_binary64_3505`
7×	`distribute-lft-out_binary64_3439` `log-pow_binary64_3577` `associate--l+_binary64_3425` `associate-+l+_binary64_3421`
6×	`add-exp-log_binary64_3526` `log-div_binary64_3575` `add-log-exp_binary64_3527`
5×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
4×	`add-cbrt-cube_binary64_3524`
3×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506`
2×	`associate-+l-_binary64_3423` `rem-log-exp_binary64_3529` `sum-log_binary64_3579`
1×	`diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `+-commutative_binary64_3418` `associate-+r-_binary64_3422` `sub-neg_binary64_3481` `rem-sqrt-square_binary64_3501`

Counts

4 → 89

Calls

4 calls:

15.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (*.f64 x y)))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series241.0ms (7%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (*.f64 x y)))
72.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
70.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
19.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify107.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4893	1657
1	4893	1657

prune119.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	101	3	104

Merged error: 0b

Counts

104 → 3

Compiler

Compiled 2183 to 1387 computations (36.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (.f64 x y)))
0.7b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
1.2b	(log.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
1.2b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite91.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64_3504`
65×	`sqrt-pow1_binary64_3506`
58×	`add-sqr-sqrt_binary64_3510`
54×	`pow1_binary64_3549`
52×	`sqrt-div_binary64_3505`
41×	`*-un-lft-identity_binary64_3488`
33×	`pow1/2_binary64_3568`
26×	`log-pow_binary64_3577`
20×	`add-cube-cbrt_binary64_3523`
18×	`swap-sqr_binary64_3455` `pow-prod-up_binary64_3558`
16×	`log-prod_binary64_3574`
15×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
12×	`log-div_binary64_3575`
10×	`distribute-lft-out_binary64_3439` `add-exp-log_binary64_3526` `associate-l_binary64_3429` `associate-r_binary64_3428` `pow-prod-down_binary64_3559` `pow-sqr_binary64_3461`
9×	`unswap-sqr_binary64_3456`
8×	`frac-times_binary64_3498` `rem-sqrt-square_binary64_3501`
7×	`associate-+l+_binary64_3421`
6×	`add-cbrt-cube_binary64_3524` `add-log-exp_binary64_3527`
4×	`associate-l/_binary64_3431` `associate-r/_binary64_3430` `sqr-abs_binary64_3503`
3×	`rem-log-exp_binary64_3529` `associate-+r+_binary64_3420`
2×	`associate-+l-_binary64_3423` `pow2_binary64_3569` `pow-plus_binary64_3551` `sum-log_binary64_3579` `prod-exp_binary64_3537`
1×	`rem-square-sqrt_binary64_3500` `diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `cbrt-unprod_binary64_3521` `+-commutative_binary64_3418` `associate-+r-_binary64_3422` `associate--l+_binary64_3425` `*-commutative_binary64_3419` `sqrt-unprod_binary64_3508` `sub-neg_binary64_3481`

Counts

4 → 179

Calls

4 calls:

25.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (.f64 x y)))
19.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
15.0ms	(log.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

series245.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (.f64 x y)))
73.0ms	(log.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
65.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
21.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

simplify103.0ms (3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4963	2913
1	4963	2913

prune265.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	191	3	194

Merged error: 0b

Counts

194 → 3

Compiler

Compiled 4724 to 3091 computations (34.6% saved)

regimes101.0ms (3%)

Compiler: Compiled 844 to 702 computations (16.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	21
1	41	21

end0.0ms (0%)

sample1.1s (31.9%)

Algorithm

1×

intervals

Results

380.0ms	7413×	body	128	valid
82.0ms	206×	body	1024	valid
52.0ms	228×	body	512	valid
20.0ms	151×	body	256	valid
3.0ms	45×	body	128	invalid
3.0ms	2×	body	2048	valid
0.0ms	7×	body	128	overflowed

Compiler

Compiled 323 to 269 computations (16.7% saved)

Details

analyze66.0ms (1.9%)

sample31.0ms (0.9%)

simplify225.0ms (6.6%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite18.0ms (0.5%)

series98.0ms (2.9%)

simplify105.0ms (3.1%)

prune52.0ms (1.5%)

localize10.0ms (0.3%)

rewrite18.0ms (0.5%)

series182.0ms (5.3%)

simplify96.0ms (2.8%)

prune84.0ms (2.5%)

localize10.0ms (0.3%)

rewrite35.0ms (1%)

series241.0ms (7%)

simplify107.0ms (3.1%)

prune119.0ms (3.5%)

localize14.0ms (0.4%)

rewrite91.0ms (2.7%)

series245.0ms (7.2%)

simplify103.0ms (3%)

prune265.0ms (7.7%)

regimes101.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (31.9%)

Profiling