Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	59×	body	1280	valid
7.0ms	134×	body	80	valid
6.0ms	45×	body	640	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

localize6.0ms

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))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 99

Calls

3 calls:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
29.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series420.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
183.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	430	1315
1	1394	1045
2	5001	981

prune231.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.4b

localize9.0ms

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))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
16×	`distribute-lft-out`
11×	`log-pow`
10×	`exp-prod`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 168

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
61.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
32.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
150.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
144.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	567	2459
1	1651	1917
2	5001	1581

prune378.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.4b

localize9.0ms

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))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
74×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`unpow-prod-down` `cube-prod`
9×	`distribute-lft-out--`
7×	`fma-neg`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 140

Calls

4 calls:

28.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
32.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series820.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(pow (- (cbrt (+ x 1.0)) (cbrt x)) 3)
272.0ms	(cbrt (+ x 1.0))
186.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify100.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	852	1818
1	3757	1458
2	5001	1454

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.3b

localize11.0ms

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)
29.2b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
15×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
8.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
0.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (cbrt (+ x 1.0)))
102.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
184.0ms	(cbrt x)
249.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify131.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	458	716
1	1307	661
2	4689	636
3	5001	634

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.3b

regimes81.0ms

Accuracy

99.6% (0.1b remaining)

Error of 15.3b against oracle of 15.2b and baseline of 29.9b

bsearch80.0ms

Steps

Iters	Range		Point
9	15.365363555117188	8982319.97820102	8001.070041045363
8	-48882.64719934817	-1.7081313977704333	-3618.8027686995374

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	31
1	39	31

end0.0ms

sample912.0ms

Algorithm

intervals

Results

325.0ms	1752×	body	1280	valid
202.0ms	4089×	body	80	valid
179.0ms	1192×	body	640	valid
72.0ms	649×	body	320	valid
25.0ms	318×	body	160	valid