Details

analyze266.0ms (5.8%)

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)

sample58.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	75×	body	1024	valid
11.0ms	38×	body	2048	valid
7.0ms	31×	body	512	valid
4.0ms	84×	body	128	valid
3.0ms	28×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify94.0ms (2.1%)

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

51.2b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
0.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.1b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(+.f64 (*.f64 x x) 1)

series120.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
30.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
23.0ms	(+.f64 (*.f64 x x) 1)
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4855	1001
1	4855	1001

prune78.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Error

Counts

66 → 5

Compiler

Compiled 1017 to 668 computations (34.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.0b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite25.0ms (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` `add-log-exp_binary64_3527`
7×	`unswap-sqr_binary64_3456` `add-cbrt-cube_binary64_3524`
6×	`prod-exp_binary64_3537`
4×	`cube-prod_binary64_3516` `sqr-pow_binary64_3460`
3×	`pow1_binary64_3549`
2×	`pow-exp_binary64_3556` `diff-log_binary64_3580` `cbrt-unprod_binary64_3521` `pow-to-exp_binary64_3557` `*-commutative_binary64_3419`
1×	`unpow3_binary64_3554` `flip3--_binary64_3492` `cancel-sign-sub-inv_binary64_3454` `flip--_binary64_3463` `cube-mult_binary64_3518` `associate--l+_binary64_3425` `sum-log_binary64_3579` `sub-neg_binary64_3481`

Counts

3 → 70

Calls

3 calls:

8.0ms	(*.f64 (pow.f64 x 3) 1/6)
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))

series83.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
29.0ms	(*.f64 3/40 (pow.f64 x 5))
24.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5018	1015

prune86.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	79	5	84

Error

Counts

84 → 5

Compiler

Compiled 1483 to 1149 computations (22.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
0.2b	(/.f64 3/32 (pow.f64 x 4))
0.4b	(/.f64 1/4 (*.f64 x x))
6.6b	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64_3488`
37×	`add-sqr-sqrt_binary64_3510`
27×	`times-frac_binary64_3494`
25×	`add-cube-cbrt_binary64_3523`
17×	`distribute-lft-out--_binary64_3440`
14×	`add-exp-log_binary64_3526`
13×	`cancel-sign-sub-inv_binary64_3454` `unpow-prod-down_binary64_3567` `add-log-exp_binary64_3527` `pow1_binary64_3549`
11×	`add-cbrt-cube_binary64_3524`
9×	`log-pow_binary64_3577`
8×	`distribute-lft-out_binary64_3439` `associate-/r*_binary64_3432`
6×	`diff-log_binary64_3580` `associate-/l*_binary64_3433`
5×	`difference-of-squares_binary64_3457` `associate--r+_binary64_3424` `sqr-pow_binary64_3460` `div-exp_binary64_3539`
4×	`frac-sub_binary64_3497`
3×	`flip3--_binary64_3492` `flip-+_binary64_3462` `log-prod_binary64_3574` `flip3-+_binary64_3491` `associate-+r+_binary64_3420` `flip--_binary64_3463` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522`
2×	`clear-num_binary64_3487` `frac-2neg_binary64_3499` `div-inv_binary64_3485` `sub-neg_binary64_3481`
1×	`pow-exp_binary64_3556` `cbrt-unprod_binary64_3521` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `associate--r-_binary64_3427` `associate--l+_binary64_3425` `prod-exp_binary64_3537`

Counts

4 → 126

Calls

4 calls:

24.0ms	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))
7.0ms	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
5.0ms	(/.f64 3/32 (pow.f64 x 4))
4.0ms	(/.f64 1/4 (*.f64 x x))

series175.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2))
49.0ms	(-.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x)))
21.0ms	(/.f64 3/32 (pow.f64 x 4))
16.0ms	(/.f64 1/4 (*.f64 x x))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4966	2840
1	4966	2840

prune185.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	138	5	143

Error

Counts

143 → 5

Compiler

Compiled 3346 to 2301 computations (31.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
9.0b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite108.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_3494`
97×	`*-un-lft-identity_binary64_3488`
87×	`add-sqr-sqrt_binary64_3510`
80×	`cancel-sign-sub-inv_binary64_3454`
74×	`add-cube-cbrt_binary64_3523`
42×	`associate-+r+_binary64_3420`
31×	`unpow-prod-down_binary64_3567` `cube-prod_binary64_3516`
18×	`add-log-exp_binary64_3527`
12×	`associate-/r*_binary64_3432`
11×	`sqr-pow_binary64_3460`
10×	`unpow3_binary64_3554` `add-exp-log_binary64_3526` `cube-mult_binary64_3518`
9×	`distribute-lft-out_binary64_3439`
6×	`distribute-lft-out--_binary64_3440` `add-cbrt-cube_binary64_3524` `log-prod_binary64_3574`
5×	`difference-of-squares_binary64_3457` `sum-log_binary64_3579` `pow1_binary64_3549`
4×	`diff-log_binary64_3580`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433` `div-exp_binary64_3539` `div-inv_binary64_3485`
2×	`log-div_binary64_3575` `frac-sub_binary64_3497` `associate--l+_binary64_3425` `sub-neg_binary64_3481`
1×	`pow-exp_binary64_3556` `rem-log-exp_binary64_3529` `clear-num_binary64_3487` `log-pow_binary64_3577` `flip3--_binary64_3492` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `flip--_binary64_3463` `associate-+r-_binary64_3422` `cbrt-undiv_binary64_3522`

Counts

4 → 203

Calls

4 calls:

34.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
24.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
24.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))

series106.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
23.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
23.0ms	(/.f64 1/8 (pow.f64 x 3))
21.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune256.0ms (5.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	215	5	220

Error

Counts

220 → 5

Compiler

Compiled 4392 to 3145 computations (28.4% saved)

regimes161.0ms (3.5%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Compiler

Compiled 1165 to 887 computations (23.9% saved)

bsearch37.0ms (0.8%)

Steps

Iters	Range		Point
6	0.7761437014994341	4.458122573049154	1.0126904852337015
10	-38395.577244555956	-6.566193378159182e-06	-1.071505362580263

Compiler

Compiled 1 to 1 computations (0% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	277	81
1	277	81

end0.0ms (0%)

sample2.3s (50.6%)

Algorithm

1×

intervals

Results

885.0ms	2445×	body	1024	valid
381.0ms	1202×	body	2048	valid
258.0ms	1238×	body	512	valid
113.0ms	2433×	body	128	valid
73.0ms	645×	body	256	valid
18.0ms	37×	body	4096	valid

Compiler

Compiled 403 to 310 computations (23.1% saved)

Details

analyze266.0ms (5.8%)

sample58.0ms (1.3%)

simplify94.0ms (2.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite25.0ms (0.5%)

series120.0ms (2.6%)

simplify63.0ms (1.4%)

prune78.0ms (1.7%)

localize8.0ms (0.2%)

rewrite25.0ms (0.5%)

series83.0ms (1.8%)

simplify68.0ms (1.5%)

prune86.0ms (1.9%)

localize13.0ms (0.3%)

rewrite52.0ms (1.1%)

series175.0ms (3.8%)

simplify79.0ms (1.7%)

prune185.0ms (4%)

localize12.0ms (0.3%)

rewrite108.0ms (2.4%)

series106.0ms (2.3%)

simplify90.0ms (2%)

prune256.0ms (5.6%)

regimes161.0ms (3.5%)

bsearch37.0ms (0.8%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample2.3s (50.6%)

Profiling