Details

analyze316.0ms (6.4%)

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
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample57.0ms (1.2%)

Algorithm

1×

intervals

Results

33.0ms	139×	body	8192	exit
8.0ms	206×	body	128	valid
3.0ms	21×	body	512	valid
2.0ms	29×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify276.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4824	18
1	4824	18

prune9.0ms (0.2%)

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: 13.7b

Counts

2 → 2

Compiler

Compiled 68 to 43 computations (36.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
6.2b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_3519`
48×	`add-sqr-sqrt_binary64_3541`
38×	`times-frac_binary64_3525`
23×	`add-cube-cbrt_binary64_3554`
10×	`difference-of-squares_binary64_3488`
9×	`associate-/l*_binary64_3464`
8×	`distribute-lft-out_binary64_3470`
7×	`add-cbrt-cube_binary64_3555` `associate-/r*_binary64_3463`
6×	`add-exp-log_binary64_3557`
5×	`add-log-exp_binary64_3558` `distribute-lft-out--_binary64_3471`
3×	`pow1_binary64_3580`
2×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `associate-/l/_binary64_3466` `div-exp_binary64_3570` `cbrt-undiv_binary64_3553` `div-sub_binary64_3524` `clear-num_binary64_3518` `div-inv_binary64_3516` `associate-/r/_binary64_3465` `frac-2neg_binary64_3530`
1×	`+-commutative_binary64_3449` `sum-log_binary64_3610` `flip--_binary64_3494` `associate-+r-_binary64_3453` `flip3--_binary64_3523`

Counts

3 → 91

Calls

3 calls:

20.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
5.0ms	(/.f64 x (exp.f64 wj))

series240.0ms (4.9%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
74.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
74.0ms	(/.f64 x (exp.f64 wj))

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5183	2095

prune465.0ms (9.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

Compiler

Compiled 9212 to 5122 computations (44.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 wj (+.f64 wj (.f64 x -2)))
0.0b	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_3541`
4×	`add-cbrt-cube_binary64_3555` `add-exp-log_binary64_3557` `add-log-exp_binary64_3558` `*-un-lft-identity_binary64_3519` `add-cube-cbrt_binary64_3554` `pow1_binary64_3580`
3×	`associate-r_binary64_3459` `associate-l_binary64_3460`
2×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `associate-+r+_binary64_3451` `associate-*r/_binary64_3461` `distribute-lft-in_binary64_3468` `distribute-rgt-in_binary64_3469`
1×	`+-commutative_binary64_3449` `pow-prod-down_binary64_3590` `sum-log_binary64_3610` `prod-exp_binary64_3568` `cbrt-unprod_binary64_3552` `unswap-sqr_binary64_3487` `*-commutative_binary64_3450`

Counts

2 → 35

Calls

2 calls:

6.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
4.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

series118.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

67.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
51.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

simplify60.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4986	598
1	4986	598

prune69.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	40	7	47

Merged error: 0.3b

Counts

47 → 7

Compiler

Compiled 1337 to 843 computations (36.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (*.f64 wj 1)))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1))))
6.2b	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1)))))

rewrite66.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_3541`
44×	`*-un-lft-identity_binary64_3519`
38×	`times-frac_binary64_3525`
30×	`associate-l_binary64_3460`
24×	`add-cube-cbrt_binary64_3554`
11×	`add-cbrt-cube_binary64_3555` `add-log-exp_binary64_3558`
10×	`add-exp-log_binary64_3557`
8×	`difference-of-squares_binary64_3488`
6×	`pow1_binary64_3580` `distribute-lft-out_binary64_3470`
5×	`flip-+_binary64_3493` `flip3-+_binary64_3522`
4×	`associate-+r+_binary64_3451` `distribute-lft-out--_binary64_3471`
3×	`associate-/r_binary64_3463` `associate-r_binary64_3459` `sum-log_binary64_3610` `associate-/l_binary64_3464`
2×	`+-commutative_binary64_3449` `div-exp_binary64_3570` `cbrt-undiv_binary64_3553` `prod-exp_binary64_3568` `frac-times_binary64_3529` `div-inv_binary64_3516` `associate-*r/_binary64_3461` `distribute-lft-in_binary64_3468` `cbrt-unprod_binary64_3552` `associate-/r/_binary64_3465` `unswap-sqr_binary64_3487` `distribute-rgt-in_binary64_3469`
1×	`associate-l/_binary64_3462` `pow-prod-down_binary64_3590` `diff-log_binary64_3611` `clear-num_binary64_3518` `cancel-sign-sub-inv_binary64_3485` `sub-neg_binary64_3512` `associate-+r-_binary64_3453` `-commutative_binary64_3450` `frac-2neg_binary64_3530`

Counts

4 → 110

Calls

4 calls:

30.0ms	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1))))
10.0ms	(+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (*.f64 wj 1)))
8.0ms	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1)))))
5.0ms	(/.f64 x (exp.f64 wj))

series480.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(+.f64 wj (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1)))))
181.0ms	(.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 1 (pow.f64 wj 3))) (+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (.f64 wj 1))))
60.0ms	(/.f64 x (exp.f64 wj))
19.0ms	(+.f64 (.f64 wj wj) (-.f64 (.f64 1 1) (*.f64 wj 1)))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	3159
1	4958	3159

prune212.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	121	8	129

Merged error: 0.3b

Counts

129 → 8

Compiler

Compiled 4888 to 2630 computations (46.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 x (exp.f64 (neg.f64 wj)))
0.0b	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
6.2b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_3519`
16×	`add-sqr-sqrt_binary64_3541`
14×	`add-cube-cbrt_binary64_3554`
12×	`times-frac_binary64_3525`
7×	`add-cbrt-cube_binary64_3555`
6×	`add-exp-log_binary64_3557`
5×	`add-log-exp_binary64_3558` `pow1_binary64_3580` `distribute-lft-out_binary64_3470`
4×	`associate-/r*_binary64_3463`
3×	`associate-r_binary64_3459` `associate-l_binary64_3460` `associate-/l*_binary64_3464`
2×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `exp-neg_binary64_3566` `associate-/l/_binary64_3466` `div-sub_binary64_3524` `associate-*r/_binary64_3461` `associate-/r/_binary64_3465`
1×	`un-div-inv_binary64_3517` `+-commutative_binary64_3449` `pow-prod-down_binary64_3590` `exp-diff_binary64_3567` `div-exp_binary64_3570` `cbrt-undiv_binary64_3553` `sum-log_binary64_3610` `prod-exp_binary64_3568` `flip--_binary64_3494` `clear-num_binary64_3518` `div-inv_binary64_3516` `cbrt-unprod_binary64_3552` `associate-+r-_binary64_3453` `unswap-sqr_binary64_3487` `neg-sub0_binary64_3514` `flip3--_binary64_3523` `*-commutative_binary64_3450` `frac-2neg_binary64_3530`

Counts

3 → 70

Calls

3 calls:

16.0ms	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
14.0ms	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
8.0ms	(*.f64 x (exp.f64 (neg.f64 wj)))

series217.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
77.0ms	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
48.0ms	(*.f64 x (exp.f64 (neg.f64 wj)))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4972	1462
1	4972	1462

prune64.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	79	8	87

Merged error: 0.3b

Counts

87 → 8

Compiler

Compiled 1491 to 606 computations (59.4% saved)

regimes71.0ms (1.4%)

Compiler: Compiled 506 to 312 computations (38.3% saved)

bsearch22.0ms (0.4%)

Steps

Iters	Range		Point
9	6.693902584847432e-16	2.3144770122914598e-10	2.2934667891059738e-10

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	39
1	36	39

end0.0ms (0%)

sample1.8s (37.3%)

Algorithm

1×

intervals

Results

924.0ms	3948×	body	8192	exit
259.0ms	6522×	body	128	valid
88.0ms	700×	body	512	valid
66.0ms	755×	body	256	valid
4.0ms	23×	body	1024	valid
4.0ms	85×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 311 to 192 computations (38.3% saved)

Details

analyze316.0ms (6.4%)

sample57.0ms (1.2%)

simplify276.0ms (5.6%)

prune9.0ms (0.2%)

localize8.0ms (0.2%)

rewrite50.0ms (1%)

series240.0ms (4.9%)

simplify52.0ms (1.1%)

prune465.0ms (9.4%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series118.0ms (2.4%)

simplify60.0ms (1.2%)

prune69.0ms (1.4%)

localize16.0ms (0.3%)

rewrite66.0ms (1.3%)

series480.0ms (9.7%)

simplify78.0ms (1.6%)

prune212.0ms (4.3%)

localize9.0ms (0.2%)

rewrite44.0ms (0.9%)

series217.0ms (4.4%)

simplify68.0ms (1.4%)

prune64.0ms (1.3%)

regimes71.0ms (1.4%)

bsearch22.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (37.3%)

Profiling