Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	54×	body	1280	valid
4.0ms	40×	body	640	valid
3.0ms	128×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	8×	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite13.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series416.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
149.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify159.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (29.0ms)

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

prune150.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	43	10	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	10	54

Merged error: 11.0b

Counts

54 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
11.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `cbrt-div`
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 → 90

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
13.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series529.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
108.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
178.0ms	(cbrt x)
154.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify54.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	420	880
1	1572	820
2	5001	760

prune283.0ms

Filtered

102 candidates to 71 candidates (69.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 11.0b

Counts

112 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
11.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
49×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
24×	`cbrt-div`
21×	`add-cube-cbrt`
18×	`pow1` `swap-sqr`
14×	`associate-r` `associate-l`
13×	`pow1/3`
12×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`add-exp-log` `frac-times` `unswap-sqr`
6×	`add-log-exp`
4×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 129

Calls

4 calls:

10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
13.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
34.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

series539.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
102.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
177.0ms	(cbrt x)
156.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

simplify62.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	410	1332
1	1530	1241
2	5001	1136

prune403.0ms

Filtered

141 candidates to 90 candidates (63.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	140	15	155

Merged error: 11.0b

Counts

155 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
11.1b	(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

rewrite100.0ms

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` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
96.0ms	(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
184.0ms	(cbrt x)
177.0ms	(cbrt x)
183.0ms	(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	255	660
1	956	543
2	5001	506

prune194.0ms

Filtered

58 candidates to 50 candidates (86.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 11.0b

Counts

73 → 15

regimes164.0ms

Accuracy

99.6% (0.1b remaining)

Error of 11.7b against oracle of 11.7b and baseline of 29.9b

bsearch94.0ms

Steps

Iters	Range		Point
8	9.788698068040235e-11	2.540201325009146e-07	2.2171874551274073e-10
10	-7.754703851107508e+72	-6.681514996074174e+59	-4.499110118396043e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	36
1	63	36
2	63	36

end0.0ms

sample592.0ms

Algorithm

intervals

Results

210.0ms	1726×	body	1280	valid
115.0ms	1230×	body	640	valid
108.0ms	4098×	body	80	valid
43.0ms	632×	body	320	valid
14.0ms	314×	body	160	valid