Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample79.0ms (1.5%)

Algorithm

1×

intervals

Results

51.0ms	141×	body	1024	valid
13.0ms	61×	body	512	valid
5.0ms	9×	body	2048	valid
3.0ms	27×	body	256	valid
1.0ms	18×	body	128	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify326.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (233.0ms)

Iter	Nodes	Cost
0	4005	15
1	4005	15

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

58.6b

Counts

2 → 1

Compiler

Compiled 20 to 18 computations (10% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 1 x) (-.f64 1 x))
6.0b	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_3488`
52×	`add-sqr-sqrt_binary64_3510`
48×	`times-frac_binary64_3494`
30×	`log-prod_binary64_3574`
25×	`add-cube-cbrt_binary64_3523`
18×	`difference-of-squares_binary64_3457`
13×	`distribute-lft-out_binary64_3439`
9×	`distribute-lft-out--_binary64_3440`
7×	`add-exp-log_binary64_3526`
6×	`associate-/r*_binary64_3432`
4×	`add-cbrt-cube_binary64_3524` `associate-/r/_binary64_3434` `associate-/l*_binary64_3433`
3×	`pow1_binary64_3549`
2×	`rem-log-exp_binary64_3529` `flip3--_binary64_3492` `associate-/l/_binary64_3435` `add-log-exp_binary64_3527` `flip--_binary64_3463` `div-exp_binary64_3539` `div-inv_binary64_3485`
1×	`clear-num_binary64_3487` `log-pow_binary64_3577` `flip-+_binary64_3462` `flip3-+_binary64_3491` `frac-2neg_binary64_3499` `log-div_binary64_3575` `cbrt-undiv_binary64_3522`

Counts

2 → 91

Calls

2 calls:

9.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))
8.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))

series65.0ms (1.2%)

Counts

2 → 14

Calls

2 calls:

43.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
22.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

Compiler

Compiled 198 to 192 computations (3% saved)

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5617	1927

prune126.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Error

0.0b

Counts

106 → 3

Compiler

Compiled 1792 to 1425 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))
0.1b	(*.f64 2/5 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 2/3)

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3510`
15×	`associate-l_binary64_3429`
13×	`add-exp-log_binary64_3526`
10×	`associate-r_binary64_3428` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
8×	`unpow-prod-down_binary64_3567`
7×	`unswap-sqr_binary64_3456` `add-cbrt-cube_binary64_3524`
6×	`prod-exp_binary64_3537`
5×	`add-log-exp_binary64_3527`
4×	`cube-prod_binary64_3516` `sqr-pow_binary64_3460`
3×	`pow1_binary64_3549`
2×	`pow-exp_binary64_3556` `cbrt-unprod_binary64_3521` `pow-to-exp_binary64_3557` `*-commutative_binary64_3419`
1×	`unpow3_binary64_3554` `flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `cube-mult_binary64_3518` `sum-log_binary64_3579`

Counts

3 → 67

Calls

3 calls:

7.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 2/5 (pow.f64 x 5))
6.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))

series169.0ms (3.2%)

Counts

3 → 12

Calls

3 calls:

93.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))
38.0ms	(*.f64 2/5 (pow.f64 x 5))
38.0ms	(*.f64 (pow.f64 x 3) 2/3)

Compiler

Compiled 339 to 279 computations (17.7% saved)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5097	919

prune94.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	79	3	82

Error

0.0b

Counts

82 → 3

Compiler

Compiled 1724 to 1254 computations (27.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x))))
6.0b	(log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x)))
6.0b	(log.f64 (sqrt.f64 (+.f64 1 x)))

rewrite59.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`*-un-lft-identity_binary64_3488`
110×	`log-prod_binary64_3574`
92×	`add-sqr-sqrt_binary64_3510`
84×	`times-frac_binary64_3494`
60×	`sqrt-prod_binary64_3504`
49×	`add-cube-cbrt_binary64_3523`
48×	`associate-+r+_binary64_3420`
28×	`difference-of-squares_binary64_3457`
19×	`distribute-lft-out_binary64_3439`
14×	`distribute-lft-out--_binary64_3440`
12×	`pow1_binary64_3549`
8×	`log-pow_binary64_3577` `add-exp-log_binary64_3526`
7×	`associate-+l+_binary64_3421`
6×	`sqrt-div_binary64_3505` `log-div_binary64_3575`
4×	`add-cbrt-cube_binary64_3524` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `add-log-exp_binary64_3527`
3×	`rem-log-exp_binary64_3529`
2×	`associate-+l-_binary64_3423` `flip3--_binary64_3492` `pow1/2_binary64_3568` `flip--_binary64_3463` `sqrt-pow1_binary64_3506` `div-inv_binary64_3485`
1×	`+-commutative_binary64_3418` `associate-+r-_binary64_3422` `div-exp_binary64_3539` `sum-log_binary64_3579` `rem-sqrt-square_binary64_3501`

Counts

4 → 168

Calls

4 calls:

22.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x))))
10.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x)))
4.0ms	(log.f64 (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

series164.0ms (3.1%)

Counts

4 → 24

Calls

4 calls:

79.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x))))
42.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 x)))
26.0ms	(log.f64 (sqrt.f64 (+.f64 1 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 608 to 529 computations (13% saved)

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4921	3749
1	4921	3749

prune290.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	192	3	195

Error

0.0b

Counts

195 → 3

Compiler

Compiled 4511 to 3692 computations (18.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
6.0b	(log.f64 (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
6.0b	(log.f64 (sqrt.f64 (-.f64 1 x)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64_3488`
79×	`add-sqr-sqrt_binary64_3510`
72×	`times-frac_binary64_3494`
66×	`sqrt-prod_binary64_3504`
51×	`log-prod_binary64_3574`
45×	`add-cube-cbrt_binary64_3523`
22×	`difference-of-squares_binary64_3457`
19×	`distribute-lft-out_binary64_3439`
11×	`distribute-lft-out--_binary64_3440`
10×	`add-exp-log_binary64_3526`
9×	`associate-/r*_binary64_3432`
8×	`sqrt-div_binary64_3505` `pow1_binary64_3549`
6×	`add-cbrt-cube_binary64_3524`
4×	`log-pow_binary64_3577` `flip3--_binary64_3492` `associate-/r/_binary64_3434` `associate-/l*_binary64_3433` `add-log-exp_binary64_3527` `flip--_binary64_3463`
3×	`rem-log-exp_binary64_3529` `log-div_binary64_3575`
2×	`associate-/l/_binary64_3435` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `div-inv_binary64_3485`
1×	`clear-num_binary64_3487` `flip-+_binary64_3462` `flip3-+_binary64_3491` `frac-2neg_binary64_3499` `cbrt-undiv_binary64_3522` `rem-sqrt-square_binary64_3501`

Counts

4 → 158

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
10.0ms	(log.f64 (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 1 x)))
4.0ms	(sqrt.f64 (-.f64 1 x))

series104.0ms (2%)

Counts

4 → 24

Calls

4 calls:

33.0ms	(log.f64 (sqrt.f64 (-.f64 1 x)))
32.0ms	(log.f64 (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
22.0ms	(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
17.0ms	(sqrt.f64 (-.f64 1 x))

Compiler

Compiled 639 to 566 computations (11.4% saved)

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5872	3460

prune281.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	182	3	185

Error

Counts

185 → 3

Compiler

Compiled 4478 to 3706 computations (17.2% saved)

regimes164.0ms (3.1%)

Accuracy

Total 0.2b remaining (93.9%)

Threshold costs 0.2b (93.9%)

Compiler

Compiled 1861 to 1615 computations (13.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	25
1	20	25

end0.0ms (0%)

sample2.8s (54.1%)

Algorithm

1×

intervals

Results

1.4s	3999×	body	1024	valid
418.0ms	1993×	body	512	valid
212.0ms	396×	body	2048	valid
125.0ms	1020×	body	256	valid
34.0ms	592×	body	128	valid

Compiler

Compiled 446 to 387 computations (13.2% saved)

Details

analyze5.0ms (0.1%)

sample79.0ms (1.5%)

simplify326.0ms (6.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite25.0ms (0.5%)

series65.0ms (1.2%)

simplify79.0ms (1.5%)

prune126.0ms (2.4%)

localize10.0ms (0.2%)

rewrite24.0ms (0.5%)

series169.0ms (3.2%)

simplify70.0ms (1.3%)

prune94.0ms (1.8%)

localize10.0ms (0.2%)

rewrite59.0ms (1.1%)

series164.0ms (3.1%)

simplify93.0ms (1.8%)

prune290.0ms (5.5%)

localize10.0ms (0.2%)

rewrite45.0ms (0.9%)

series104.0ms (2%)

simplify111.0ms (2.1%)

prune281.0ms (5.3%)

regimes164.0ms (3.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (54.1%)

Profiling