Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	53×	body	1280	valid
3.0ms	131×	body	80	valid
2.0ms	33×	body	640	valid
2.0ms	28×	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: 30.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
4.0b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite60.0ms

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:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
51.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series433.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
186.0ms	(cbrt x)
157.0ms	(- (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

prune247.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.0b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
24.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series739.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
186.0ms	(cbrt x)
185.0ms	(cbrt x)
183.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify141.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	260	403
1	906	328
2	4583	314
3	5001	311

prune241.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
4.0b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
26.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series909.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (cbrt x))
242.0ms	(cbrt (cbrt x))
243.0ms	(cbrt (cbrt x))
180.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	276	514
1	849	452
2	3939	423
3	5001	418

prune325.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
3.8b	(log1p (expm1 (cbrt (cbrt x))))
4.0b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow1/3`
1×	`sub-neg` `log1p-udef` `flip3--` `fma-neg` `diff-log` `log1p-expm1` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
0.0ms	(log1p (expm1 (cbrt (cbrt x))))
25.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (cbrt x))
242.0ms	(cbrt (cbrt x))
381.0ms	(log1p (expm1 (cbrt (cbrt x))))
179.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify116.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	289	482
1	866	420
2	3958	391
3	5001	389

prune303.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.3b

regimes77.0ms

Accuracy

99% (0.2b remaining)

Error of 12.0b against oracle of 11.8b and baseline of 29.9b

bsearch111.0ms

Steps

Iters	Range		Point
10	26.826342714152005	1.350953981158519e+19	2677.8139172161887
9	-3.6176712773181885e+65	-2.6772928612991434e+57	-4.53999343152509e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	57
1	73	57

end0.0ms

sample537.0ms

Algorithm

intervals

Results

177.0ms	1731×	body	1280	valid
95.0ms	1233×	body	640	valid
85.0ms	4082×	body	80	valid
38.0ms	672×	body	320	valid
11.0ms	282×	body	160	valid