Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample26.0ms

Algorithm

intervals

Results

12.0ms	47×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	142×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune1.0ms

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: 26.7b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt.f64 (+.f64 x 1))
0.6b	(cbrt.f64 x)
2.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
4×	`difference-of-squares_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`cbrt-div_binary64` `distribute-lft-out_binary64` `pow1/3_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 43

Calls

3 calls:

3.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)
9.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series166.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(cbrt.f64 (+.f64 x 1))
85.0ms	(cbrt.f64 x)
58.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

simplify106.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4790	710
1	4790	710

prune59.0ms

Filtered

44 candidates to 52 candidates (-18.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Merged error: 0.2b

Counts

53 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
7.6b	(-.f64 (/.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))) (cbrt.f64 x))
13.0b	(cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
17.5b	(cbrt.f64 (+.f64 1 (pow.f64 x 3)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
10×	`difference-of-squares_binary64`
8×	`times-frac_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt.f64 x)
36.0ms	(-.f64 (/.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))) (cbrt.f64 x))
7.0ms	(cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 x 3)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt.f64 x)
71.0ms	(-.f64 (/.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))) (cbrt.f64 x))
28.0ms	(cbrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
103.0ms	(cbrt.f64 (+.f64 1 (pow.f64 x 3)))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4942	1949
1	4942	1949

prune92.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	72	5	77

Merged error: 0.2b

Counts

77 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 x 1/9) 1/3)
0.2b	(.f64 x (-.f64 (.f64 x 1/9) 1/3))
0.4b	(*.f64 x 1/9)
0.6b	(cbrt.f64 x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`sub-neg_binary64` `cbrt-prod_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(-.f64 (*.f64 x 1/9) 1/3)
7.0ms	(.f64 x (-.f64 (.f64 x 1/9) 1/3))
4.0ms	(*.f64 x 1/9)
1.0ms	(cbrt.f64 x)

series151.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(-.f64 (*.f64 x 1/9) 1/3)
33.0ms	(.f64 x (-.f64 (.f64 x 1/9) 1/3))
11.0ms	(*.f64 x 1/9)
84.0ms	(cbrt.f64 x)

simplify86.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5057	665

prune51.0ms

Filtered

51 candidates to 74 candidates (-45.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.2b

Counts

79 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cbrt.f64 x) x)
0.3b	(*.f64 (/.f64 (cbrt.f64 x) x) (+.f64 1/3 (/.f64 -1/9 x)))
0.4b	(/.f64 -1/9 x)
0.6b	(cbrt.f64 x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
47×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`
25×	`cbrt-prod_binary64`
22×	`associate-l_binary64`
13×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`cbrt-undiv_binary64` `unswap-sqr_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `pow1/3_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `pow-div_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 127

Calls

4 calls:

4.0ms	(/.f64 (cbrt.f64 x) x)
14.0ms	(*.f64 (/.f64 (cbrt.f64 x) x) (+.f64 1/3 (/.f64 -1/9 x)))
3.0ms	(/.f64 -1/9 x)
1.0ms	(cbrt.f64 x)

series357.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/.f64 (cbrt.f64 x) x)
168.0ms	(*.f64 (/.f64 (cbrt.f64 x) x) (+.f64 1/3 (/.f64 -1/9 x)))
13.0ms	(/.f64 -1/9 x)
82.0ms	(cbrt.f64 x)

simplify55.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5261	1800

prune107.0ms

Filtered

115 candidates to 139 candidates (-20.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	127	12	139
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	128	16	144

Merged error: 0.0b

Counts

144 → 16

regimes51.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.2b

bsearch31.0ms

Steps

Iters	Range		Point
10	0.1781839115170339	7491206753.695265	58716.682115847965
10	-888821.1244261832	-1.9495488771616177e-11	-58198.39330764905

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	57
1	53	57

end0.0ms

sample571.0ms

Algorithm

intervals

Results

201.0ms	1644×	body	1280	valid
118.0ms	1275×	body	640	valid
104.0ms	4146×	body	80	valid
43.0ms	633×	body	320	valid
13.0ms	302×	body	160	valid

Details

analyze1.0ms

sample26.0ms

simplify15.0ms

prune1.0ms

localize5.0ms

rewrite15.0ms

series166.0ms

simplify106.0ms

prune59.0ms

localize13.0ms

rewrite55.0ms

series285.0ms

simplify108.0ms

prune92.0ms

localize10.0ms

rewrite18.0ms

series151.0ms

simplify86.0ms

prune51.0ms

localize7.0ms

rewrite27.0ms

series357.0ms

simplify55.0ms

prune107.0ms

regimes51.0ms

bsearch31.0ms

simplify5.0ms

end0.0ms

sample571.0ms

Profiling