Details

analyze348.0ms (5.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Symmetry

Compiler

Compiled 10 to 8 computations (20% saved)

sample63.0ms (0.9%)

Algorithm

1×

intervals

Results

27.0ms	81×	body	1024	valid
11.0ms	37×	body	2048	valid
9.0ms	45×	body	512	valid
4.0ms	75×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0%)

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

52.7b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.8b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.1b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite67.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

52.4b

Rules

9×	`*-un-lft-identity_binary64_3488`
6×	`add-sqr-sqrt_binary64_3510`
5×	`pow1_binary64_3549` `add-log-exp_binary64_3527` `add-cube-cbrt_binary64_3523`
4×	`add-exp-log_binary64_3526` `log-prod_binary64_3574`
3×	`add-cbrt-cube_binary64_3524` `flip3-+_binary64_3491` `flip-+_binary64_3462` `sqrt-prod_binary64_3504`
2×	`sqrt-div_binary64_3505` `log-div_binary64_3575` `distribute-lft-out_binary64_3439`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501` `log-pow_binary64_3577` `rem-log-exp_binary64_3529` `sum-log_binary64_3579` `+-commutative_binary64_3418`

Counts

3 → 42

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 766 to 464 computations (39.4% saved)

series242.0ms (3.6%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

104.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
57.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
44.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 963 to 825 computations (14.3% saved)

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5201	1166

prune73.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Error

0.0b

Counts

76 → 5

Compiler

Compiled 1089 to 731 computations (32.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5/112 (pow.f64 x 7))
0.1b	(*.f64 (pow.f64 x 5) 3/40)
0.1b	(*.f64 (pow.f64 x 3) 1/6)
23.6b	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))

rewrite232.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-sqr-sqrt_binary64_3510`
22×	`associate-l_binary64_3429`
19×	`add-exp-log_binary64_3526`
17×	`*-un-lft-identity_binary64_3488`
16×	`add-log-exp_binary64_3527`
15×	`add-cube-cbrt_binary64_3523`
13×	`associate-r_binary64_3428`
12×	`unpow-prod-down_binary64_3567`
10×	`add-cbrt-cube_binary64_3524` `unswap-sqr_binary64_3456`
9×	`prod-exp_binary64_3537`
6×	`sqr-pow_binary64_3460`
4×	`sum-log_binary64_3579` `diff-log_binary64_3580` `pow1_binary64_3549` `flip3-+_binary64_3491` `frac-sub_binary64_3497` `flip-+_binary64_3462` `cube-prod_binary64_3516`
3×	`cancel-sign-sub-inv_binary64_3454` `pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `cbrt-unprod_binary64_3521` `*-commutative_binary64_3419`
1×	`flip3--_binary64_3492` `sub-neg_binary64_3481` `flip--_binary64_3463` `difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `associate--l+_binary64_3425` `associate--r+_binary64_3424` `unpow3_binary64_3554` `cube-mult_binary64_3518`

Counts

4 → 106

Calls

4 calls:

11.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(*.f64 5/112 (pow.f64 x 7))
5.0ms	(*.f64 (pow.f64 x 5) 3/40)

Compiler

Compiled 3201 to 2555 computations (20.2% saved)

series185.0ms (2.7%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

53.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
45.0ms	(*.f64 5/112 (pow.f64 x 7))
40.0ms	(*.f64 (pow.f64 x 5) 3/40)
34.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 691 to 574 computations (16.9% saved)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4923	2212
1	4923	2212

prune198.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	123	5	128

Error

Counts

128 → 5

Compiler

Compiled 3197 to 2531 computations (20.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (pow.f64 x 7) -5/112)
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 1/6 (pow.f64 x 3))
23.6b	(+.f64 (.f64 3/40 (pow.f64 x 5)) (-.f64 (.f64 (pow.f64 x 7) -5/112) (*.f64 1/6 (pow.f64 x 3))))

rewrite179.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64_3510`
22×	`associate-r_binary64_3428`
19×	`add-exp-log_binary64_3526`
14×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
13×	`associate-l_binary64_3429`
12×	`unpow-prod-down_binary64_3567`
10×	`add-cbrt-cube_binary64_3524` `unswap-sqr_binary64_3456`
9×	`add-log-exp_binary64_3527` `prod-exp_binary64_3537`
6×	`sqr-pow_binary64_3460`
4×	`pow1_binary64_3549` `cube-prod_binary64_3516`
3×	`pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `cbrt-unprod_binary64_3521` `*-commutative_binary64_3419`
2×	`sum-log_binary64_3579` `associate-+r+_binary64_3420`
1×	`diff-log_binary64_3580` `flip3-+_binary64_3491` `flip-+_binary64_3462` `associate-+r-_binary64_3422` `sub-neg_binary64_3481` `cancel-sign-sub-inv_binary64_3454` `+-commutative_binary64_3418` `unpow3_binary64_3554` `cube-mult_binary64_3518`

Counts

4 → 96

Calls

4 calls:

11.0ms	(+.f64 (.f64 3/40 (pow.f64 x 5)) (-.f64 (.f64 (pow.f64 x 7) -5/112) (*.f64 1/6 (pow.f64 x 3))))
6.0ms	(*.f64 1/6 (pow.f64 x 3))
5.0ms	(*.f64 3/40 (pow.f64 x 5))
5.0ms	(*.f64 (pow.f64 x 7) -5/112)

Compiler

Compiled 2535 to 2028 computations (20% saved)

series214.0ms (3.2%)

Error

Counts

4 → 14

Calls

4 calls:

65.0ms	(+.f64 (.f64 3/40 (pow.f64 x 5)) (-.f64 (.f64 (pow.f64 x 7) -5/112) (*.f64 1/6 (pow.f64 x 3))))
53.0ms	(*.f64 (pow.f64 x 7) -5/112)
44.0ms	(*.f64 3/40 (pow.f64 x 5))
37.0ms	(*.f64 1/6 (pow.f64 x 3))

Compiler

Compiled 664 to 547 computations (17.6% saved)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5407	1402

prune154.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Error

Counts

115 → 5

Compiler

Compiled 2652 to 2098 computations (20.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1/16 (pow.f64 x 5))
14.1b	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
19.3b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
22.5b	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))

rewrite487.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

80×	`*-un-lft-identity_binary64_3488`
40×	`times-frac_binary64_3494`
36×	`add-sqr-sqrt_binary64_3510`
23×	`add-cube-cbrt_binary64_3523`
18×	`add-log-exp_binary64_3527` `distribute-lft-out_binary64_3439`
13×	`frac-add_binary64_3496` `unpow-prod-down_binary64_3567`
10×	`add-exp-log_binary64_3526` `cancel-sign-sub-inv_binary64_3454`
9×	`frac-sub_binary64_3497` `distribute-lft-out--_binary64_3440`
7×	`log-div_binary64_3575` `log-prod_binary64_3574` `associate-/r*_binary64_3432`
6×	`add-cbrt-cube_binary64_3524` `associate-+l+_binary64_3421`
5×	`sum-log_binary64_3579` `pow1_binary64_3549` `flip3-+_binary64_3491` `flip-+_binary64_3462` `difference-of-squares_binary64_3457` `sqr-pow_binary64_3460`
4×	`diff-log_binary64_3580`
3×	`flip3--_binary64_3492` `flip--_binary64_3463` `div-exp_binary64_3539` `associate-/l*_binary64_3433`
2×	`sub-neg_binary64_3481`
1×	`associate-+l-_binary64_3423` `+-commutative_binary64_3418` `cube-prod_binary64_3516` `associate--r+_binary64_3424` `log-pow_binary64_3577` `rem-log-exp_binary64_3529` `pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `cbrt-undiv_binary64_3522` `frac-2neg_binary64_3499` `clear-num_binary64_3487` `div-inv_binary64_3485`

Counts

4 → 126

Calls

4 calls:

55.0ms	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
55.0ms	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))
42.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

Compiler

Compiled 4941 to 4063 computations (17.8% saved)

series266.0ms (3.9%)

Error

Counts

4 → 26

Calls

4 calls:

87.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
62.0ms	(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7)))
47.0ms	(log.f64 (+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 5/128 (pow.f64 x 7))))
44.0ms	(/.f64 1/16 (pow.f64 x 5))

Compiler

Compiled 1088 to 960 computations (11.8% saved)

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4832	4820
1	4832	4820

prune315.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	152	5	157

Error

Counts

157 → 5

Compiler

Compiled 4752 to 3881 computations (18.3% saved)

regimes323.0ms (4.8%)

Accuracy

Total 0.1b remaining (97%)

Threshold costs 0.1b (97%)

Compiler

Compiled 3122 to 2447 computations (21.6% saved)

bsearch36.0ms (0.5%)

Steps

Iters	Range		Point
8	0.0052590484079004405	283.59753326053533	1.0731388620338205
7	-61.85560394846114	-0.6645254606628889	-1.0255598703715518

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	227	100
1	227	100

Removed

()

end0.0ms (0%)

sample3.0s (44.2%)

Algorithm

1×

intervals

Results

915.0ms	2529×	body	1024	valid
373.0ms	1200×	body	2048	valid
245.0ms	1189×	body	512	valid
109.0ms	2374×	body	128	valid
76.0ms	652×	body	256	valid
25.0ms	56×	body	4096	valid

Compiler

Compiled 1057 to 836 computations (20.9% saved)

Details

analyze348.0ms (5.1%)

sample63.0ms (0.9%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite67.0ms (1%)

series242.0ms (3.6%)

simplify68.0ms (1%)

prune73.0ms (1.1%)

localize15.0ms (0.2%)

rewrite232.0ms (3.4%)

series185.0ms (2.7%)

simplify79.0ms (1.2%)

prune198.0ms (2.9%)

localize12.0ms (0.2%)

rewrite179.0ms (2.6%)

series214.0ms (3.2%)

simplify73.0ms (1.1%)

prune154.0ms (2.3%)

localize15.0ms (0.2%)

rewrite487.0ms (7.2%)

series266.0ms (3.9%)

simplify119.0ms (1.8%)

prune315.0ms (4.6%)

regimes323.0ms (4.8%)

bsearch36.0ms (0.5%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.0s (44.2%)

Profiling