Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	67×	body	1280	valid
3.0ms	36×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	11×	body	320	valid
0.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
38.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series398.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(cbrt (+ x 1.0))
172.0ms	(cbrt x)
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify156.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	287	358
1	934	344
2	4833	322
3	5001	322

prune147.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.8b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`cbrt-prod`
11×	`log-pow`
10×	`exp-prod`
8×	`add-cube-cbrt` `difference-of-squares`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
83.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
41.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series541.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
138.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	336	568
1	1025	536
2	5001	505

prune240.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.8b	(log (exp (- (* 1 (cbrt (+ x 1.0))) (cbrt x))))
2.2b	(- (* 1 (cbrt (+ x 1.0))) (cbrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-log-exp`
5×	`pow1` `log-prod` `log-pow`
4×	`add-exp-log` `exp-prod` `add-cbrt-cube`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum` `distribute-lft-out--`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
34.0ms	(log (exp (- (* 1 (cbrt (+ x 1.0))) (cbrt x))))
14.0ms	(- (* 1 (cbrt (+ x 1.0))) (cbrt x))

series536.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ x 1.0))
171.0ms	(cbrt x)
137.0ms	(log (exp (- (* 1 (cbrt (+ x 1.0))) (cbrt x))))
143.0ms	(- (* 1 (cbrt (+ x 1.0))) (cbrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	320	523
1	1058	474
2	5002	456

prune221.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
9.6b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

36.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
40.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series509.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
85.0ms	(cbrt (cbrt (+ x 1.0)))
182.0ms	(cbrt x)
143.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify59.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	514	926
1	1920	862
2	5002	810

prune279.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.8b

regimes70.0ms

Accuracy

99% (0.2b remaining)

Error of 11.6b against oracle of 11.5b and baseline of 29.6b

bsearch83.0ms

Steps

Iters	Range		Point
9	1.3330246063773173e-09	3.618674152218468	6.8995689301126785e-09
10	-8.315572451848708e+66	-2.678000396648453e+52	-4.4502080277561566e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	37
1	61	37
2	61	37

end0.0ms

sample519.0ms

Algorithm

intervals

Results

164.0ms	1700×	body	1280	valid
100.0ms	1254×	body	640	valid
82.0ms	4116×	body	80	valid
36.0ms	605×	body	320	valid
12.0ms	325×	body	160	valid