Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	59×	body	1280	valid
6.0ms	45×	body	640	valid
6.0ms	134×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	5×	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: 29.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite26.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
23.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series411.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(cbrt (+ x 1.0))
175.0ms	(cbrt x)
147.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify157.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

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

prune159.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.1b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
1.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite82.0ms

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:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
51.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
26.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series566.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
150.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

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

prune250.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
31×	`cbrt-prod`
12×	`difference-of-squares`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`distribute-lft-out`
3×	`pow-unpow`
2×	`cube-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

27.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
22.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series625.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
87.0ms	(cbrt (+ x 1.0))
180.0ms	(cbrt x)
145.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify75.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	694	859
1	3138	808
2	5001	804

prune276.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt x)
10.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
15×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
7.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.0ms	(cbrt x)
20.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series520.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (cbrt (+ x 1.0)))
102.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
182.0ms	(cbrt x)
149.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify47.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	477	746
1	1545	691
2	5002	672

prune242.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.3b

regimes71.0ms

Accuracy

98.3% (0.4b remaining)

Error of 8.9b against oracle of 8.5b and baseline of 30.0b

bsearch72.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	2.8739991244123034e-09
8	-48882.64719934817	-1.7081313977704333	-3618.8027686995374

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	34
1	54	34
2	54	34

end0.0ms

sample893.0ms

Algorithm

intervals

Results

317.0ms	1752×	body	1280	valid
203.0ms	4089×	body	80	valid
171.0ms	1192×	body	640	valid
73.0ms	649×	body	320	valid
25.0ms	318×	body	160	valid