Details

sample102.0ms

Algorithm

intervals

Results

43.0ms	103×	body	2560	valid
24.0ms	85×	body	1280	valid
13.0ms	235×	body	80	nan
6.0ms	28×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	9×	body	80	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7

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: 0.7b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
29.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune154.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 0.7b

Counts

79 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

0.7b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify99.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	93
1	54	82
2	153	82
3	423	82
4	1909	82
5	5001	82

prune45.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	14	4	18

Merged error: 0.7b

Counts

18 → 4

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.7b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `expm1-log1p` `expm1-udef`

Counts

2 → 21

Calls

2 calls:

1.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
1.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
7.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify100.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	187
1	66	165
2	165	165
3	435	165
4	1921	165
5	5001	165

prune67.0ms

Filtered

27 candidates to 17 candidates (63.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	26	5	31

Merged error: 0.7b

Counts

31 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b	(exp (log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.7b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `exp-prod`
3×	`expm1-log1p-u` `exp-sum` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-pow`
1×	`acos-asin` `rem-log-exp` `rem-exp-log`

Counts

3 → 41

Calls

3 calls:

1.0ms	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
2.0ms	(exp (log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
1.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
6.0ms	(exp (log (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
7.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify178.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	70	388
1	116	346
2	246	334
3	702	328
4	4008	328
5	5001	328

prune109.0ms

Filtered

50 candidates to 32 candidates (64.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	50	5	55

Merged error: 0.7b

Counts

55 → 5

regimes28.0ms

Accuracy

0% (0.0b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	2973×	body	2560	valid
717.0ms	2524×	body	1280	valid
315.0ms	8042×	body	80	nan
263.0ms	1263×	body	640	valid
96.0ms	629×	body	320	valid
48.0ms	413×	body	160	valid
12.0ms	198×	body	80	valid