Details

analyze316.0ms (5.3%)

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)

sample48.0ms (0.8%)

Algorithm

1×

intervals

Results

26.0ms	111×	body	8192	exit
8.0ms	212×	body	128	valid
3.0ms	25×	body	512	valid
1.0ms	18×	body	256	valid
0.0ms	1×	body	1024	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify221.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4887	18
1	4887	18

prune4.0ms (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

Error

14.1b

Counts

2 → 2

Compiler

Compiled 40 to 26 computations (35% saved)

localize8.0ms (0.1%)

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))
5.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_3488`
48×	`add-sqr-sqrt_binary64_3510`
38×	`times-frac_binary64_3494`
23×	`add-cube-cbrt_binary64_3523`
10×	`difference-of-squares_binary64_3457`
9×	`associate-/l*_binary64_3433`
8×	`distribute-lft-out_binary64_3439`
7×	`associate-/r*_binary64_3432` `add-cbrt-cube_binary64_3524`
6×	`add-exp-log_binary64_3526`
5×	`distribute-lft-out--_binary64_3440` `add-log-exp_binary64_3527`
3×	`pow1_binary64_3549`
2×	`clear-num_binary64_3487` `associate-/l/_binary64_3435` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-sub_binary64_3493` `div-inv_binary64_3485`
1×	`flip3--_binary64_3492` `+-commutative_binary64_3418` `flip--_binary64_3463` `associate-+r-_binary64_3422` `sum-log_binary64_3579`

Counts

3 → 91

Calls

3 calls:

23.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))

series124.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
39.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
37.0ms	(/.f64 x (exp.f64 wj))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4946	2095
1	4946	2095

prune105.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	5	102

Error

0.7b

Counts

102 → 5

Compiler

Compiled 2102 to 858 computations (59.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_3510`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527` `*-un-lft-identity_binary64_3488` `pow1_binary64_3549`
3×	`associate-l_binary64_3429` `associate-r_binary64_3428`
2×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-+r+_binary64_3420` `associate-*r/_binary64_3430`
1×	`unswap-sqr_binary64_3456` `cbrt-unprod_binary64_3521` `+-commutative_binary64_3418` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419` `sum-log_binary64_3579` `prod-exp_binary64_3537`

Counts

2 → 35

Calls

2 calls:

6.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
3.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

series58.0ms (1%)

Counts

2 → 6

Calls

2 calls:

33.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
25.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4970	598
1	4970	598

prune44.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	37	9	46

Error

0.7b

Counts

46 → 9

Compiler

Compiled 801 to 486 computations (39.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
10.0b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.0b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.0b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`associate-*r/_binary64_3430`
18×	`cbrt-div_binary64_3520`
11×	`pow1_binary64_3549`
10×	`add-sqr-sqrt_binary64_3510`
9×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `pow1/3_binary64_3570`
8×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
7×	`cbrt-prod_binary64_3519`
6×	`add-exp-log_binary64_3526`
4×	`swap-sqr_binary64_3455` `add-cbrt-cube_binary64_3524` `associate-l_binary64_3429` `frac-times_binary64_3498` `associate-r_binary64_3428` `add-log-exp_binary64_3527`
2×	`associate-*l/_binary64_3431` `pow-prod-up_binary64_3558` `pow-prod-down_binary64_3559` `pow-sqr_binary64_3461`
1×	`unswap-sqr_binary64_3456` `cbrt-unprod_binary64_3521` `pow2_binary64_3569` `pow-plus_binary64_3551` `*-commutative_binary64_3419` `prod-exp_binary64_3537`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

series862.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(.f64 (cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2)))) (cbrt.f64 (.f64 wj (+.f64 wj (*.f64 x -2)))))
204.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
204.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
203.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5129	1497

prune136.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	82	11	93

Error

0.7b

Counts

93 → 11

Compiler

Compiled 2909 to 1940 computations (33.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
0.6b	(cbrt.f64 wj)
10.0b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
10.0b	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64_3519`
6×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `cbrt-div_binary64_3520` `*-un-lft-identity_binary64_3488`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `associate-*r/_binary64_3430` `add-log-exp_binary64_3527` `pow1/3_binary64_3570` `pow1_binary64_3549`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491`

Counts

4 → 46

Calls

4 calls:

4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
4.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
3.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
1.0ms	(cbrt.f64 wj)

series637.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
203.0ms	(cbrt.f64 (.f64 wj (+.f64 wj (.f64 x -2))))
124.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
84.0ms	(cbrt.f64 wj)

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4904	793
1	4904	793

prune89.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	58	11	69

Error

0.7b

Counts

69 → 11

Compiler

Compiled 1976 to 1276 computations (35.4% saved)

regimes265.0ms (4.5%)

Accuracy

Total 0.5b remaining (63.1%)

Threshold costs 0.5b (63.1%)

Compiler

Compiled 3291 to 2142 computations (34.9% saved)

bsearch3.0ms (0%)

Compiler: Compiled 16 to 8 computations (50% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	444	63
1	444	63

end0.0ms (0%)

sample2.6s (43.3%)

Algorithm

1×

intervals

Results

833.0ms	3726×	body	8192	exit
281.0ms	701×	body	512	valid
260.0ms	6523×	body	128	valid
60.0ms	753×	body	256	valid
4.0ms	23×	body	1024	valid
3.0ms	77×	body	128	invalid
0.0ms	14×	body	128	overflowed

Compiler

Compiled 1160 to 752 computations (35.2% saved)

Details

analyze316.0ms (5.3%)

sample48.0ms (0.8%)

simplify221.0ms (3.7%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite48.0ms (0.8%)

series124.0ms (2.1%)

simplify76.0ms (1.3%)

prune105.0ms (1.8%)

localize5.0ms (0.1%)

rewrite11.0ms (0.2%)

series58.0ms (1%)

simplify55.0ms (0.9%)

prune44.0ms (0.7%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series862.0ms (14.6%)

simplify81.0ms (1.4%)

prune136.0ms (2.3%)

localize13.0ms (0.2%)

rewrite17.0ms (0.3%)

series637.0ms (10.8%)

simplify67.0ms (1.1%)

prune89.0ms (1.5%)

regimes265.0ms (4.5%)

bsearch3.0ms (0%)

simplify16.0ms (0.3%)

end0.0ms (0%)

sample2.6s (43.3%)

Profiling