Details

analyze274.0ms (5.7%)

Algorithm

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample66.0ms (1.4%)

Algorithm

1×

intervals

Results

32.0ms	86×	body	1024	valid
15.0ms	47×	body	2048	valid
6.0ms	31×	body	512	valid
3.0ms	70×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune3.0ms (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: 54.8b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.6b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.6b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

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)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series91.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

46.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
25.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
19.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5224	862

prune76.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.0b

Counts

52 → 5

Compiler

Compiled 833 to 553 computations (33.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.2b	(*.f64 (pow.f64 x 3) 1/6)
0.5b	(*.f64 3/40 (pow.f64 x 5))
19.3b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3510`
15×	`associate-l_binary64_3429`
14×	`add-exp-log_binary64_3526`
11×	`add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527` `*-un-lft-identity_binary64_3488`
10×	`associate-r_binary64_3428`
8×	`add-cbrt-cube_binary64_3524` `unpow-prod-down_binary64_3567`
7×	`unswap-sqr_binary64_3456`
6×	`prod-exp_binary64_3537`
4×	`cube-prod_binary64_3516` `sqr-pow_binary64_3460` `pow1_binary64_3549`
2×	`pow-exp_binary64_3556` `diff-log_binary64_3580` `cbrt-unprod_binary64_3521` `pow-to-exp_binary64_3557` `*-commutative_binary64_3419` `sum-log_binary64_3579`
1×	`unpow3_binary64_3554` `flip3--_binary64_3492` `flip-+_binary64_3462` `flip3-+_binary64_3491` `cancel-sign-sub-inv_binary64_3454` `+-commutative_binary64_3418` `flip--_binary64_3463` `cube-mult_binary64_3518` `associate--l+_binary64_3425` `sub-neg_binary64_3481`

Counts

4 → 81

Calls

4 calls:

6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series171.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
32.0ms	(*.f64 3/40 (pow.f64 x 5))
31.0ms	(*.f64 (pow.f64 x 3) 1/6)
29.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5121	1217

prune105.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

Compiler

Compiled 1744 to 1353 computations (22.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6)))
0.2b	(*.f64 (pow.f64 x 3) 1/6)
0.5b	(*.f64 3/40 (pow.f64 x 5))
19.3b	(-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3510`
15×	`associate-l_binary64_3429`
14×	`add-exp-log_binary64_3526`
13×	`*-un-lft-identity_binary64_3488`
11×	`add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527`
10×	`associate-r_binary64_3428`
8×	`add-cbrt-cube_binary64_3524` `unpow-prod-down_binary64_3567`
7×	`unswap-sqr_binary64_3456`
6×	`prod-exp_binary64_3537`
4×	`cube-prod_binary64_3516` `sqr-pow_binary64_3460` `pow1_binary64_3549`
2×	`pow-exp_binary64_3556` `diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `cbrt-unprod_binary64_3521` `associate-+r+_binary64_3420` `pow-to-exp_binary64_3557` `*-commutative_binary64_3419` `sum-log_binary64_3579` `sub-neg_binary64_3481`
1×	`unpow3_binary64_3554` `distribute-lft-out_binary64_3439` `flip3--_binary64_3492` `flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `flip--_binary64_3463` `associate-+r-_binary64_3422` `cube-mult_binary64_3518`

Counts

4 → 84

Calls

4 calls:

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

series176.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6))
31.0ms	(*.f64 3/40 (pow.f64 x 5))
28.0ms	(+.f64 x (-.f64 (.f64 3/40 (pow.f64 x 5)) (.f64 (pow.f64 x 3) 1/6)))
23.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify93.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5185	1361

prune108.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

Compiler

Compiled 1804 to 1404 computations (22.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/8 (pow.f64 x 3))
0.4b	(/.f64 1/16 (pow.f64 x 5))
12.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
18.4b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite114.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_3488`
73×	`add-sqr-sqrt_binary64_3510` `times-frac_binary64_3494`
47×	`add-cube-cbrt_binary64_3523`
26×	`unpow-prod-down_binary64_3567`
19×	`associate-/r*_binary64_3432`
15×	`add-exp-log_binary64_3526`
14×	`cube-prod_binary64_3516`
11×	`log-prod_binary64_3574`
10×	`difference-of-squares_binary64_3457` `sqr-pow_binary64_3460`
9×	`add-log-exp_binary64_3527`
8×	`add-cbrt-cube_binary64_3524`
6×	`distribute-lft-out_binary64_3439` `distribute-lft-out--_binary64_3440` `associate-/l*_binary64_3433` `frac-sub_binary64_3497` `div-exp_binary64_3539`
5×	`cancel-sign-sub-inv_binary64_3454` `log-div_binary64_3575` `pow1_binary64_3549`
4×	`unpow3_binary64_3554` `cube-mult_binary64_3518`
2×	`pow-exp_binary64_3556` `clear-num_binary64_3487` `frac-add_binary64_3496` `flip3--_binary64_3492` `flip-+_binary64_3462` `diff-log_binary64_3580` `flip3-+_binary64_3491` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `flip--_binary64_3463` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
1×	`rem-log-exp_binary64_3529` `log-pow_binary64_3577` `associate--r+_binary64_3424` `sum-log_binary64_3579` `sub-neg_binary64_3481`

Counts

4 → 164

Calls

4 calls:

45.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
39.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
8.0ms	(/.f64 1/16 (pow.f64 x 5))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series120.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
30.0ms	(/.f64 1/16 (pow.f64 x 5))
27.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
22.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5284	3670

prune277.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	176	5	181

Merged error: 0.0b

Counts

181 → 5

Compiler

Compiled 4148 to 3300 computations (20.4% saved)

regimes193.0ms (4%)

Compiler: Compiled 1422 to 1081 computations (24% saved)

bsearch38.0ms (0.8%)

Steps

Iters	Range		Point
10	0.010650040958805266	6160599998.382685	0.9534316566480352
7	-51.73968711192573	-0.2744891438179246	-1.0657959477224437

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.4s (50.7%)

Algorithm

1×

intervals

Results

971.0ms	2660×	body	1024	valid
364.0ms	1131×	body	2048	valid
247.0ms	1177×	body	512	valid
108.0ms	2347×	body	128	valid
73.0ms	643×	body	256	valid
19.0ms	42×	body	4096	valid

Compiler

Compiled 479 to 367 computations (23.4% saved)

Details

analyze274.0ms (5.7%)

sample66.0ms (1.4%)

simplify98.0ms (2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series91.0ms (1.9%)

simplify68.0ms (1.4%)

prune76.0ms (1.6%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series171.0ms (3.5%)

simplify90.0ms (1.9%)

prune105.0ms (2.2%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series176.0ms (3.7%)

simplify93.0ms (1.9%)

prune108.0ms (2.2%)

localize12.0ms (0.2%)

rewrite114.0ms (2.4%)

series120.0ms (2.5%)

simplify99.0ms (2.1%)

prune277.0ms (5.7%)

regimes193.0ms (4%)

bsearch38.0ms (0.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (50.7%)

Profiling