Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	108×	body	2560	valid
20.0ms	74×	body	1280	valid
8.0ms	222×	body	80	nan
7.0ms	37×	body	640	valid
3.0ms	24×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	8×	body	80	valid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 0.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

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))
5.0ms	(* 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:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

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

prune149.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 0.5b

Counts

79 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.1b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `log1p-udef` `expm1-log1p` `log1p-expm1` `associate-r` `*-commutative` `expm1-udef` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

1.0ms	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(expm1 (log1p (acos (/ (- 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)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
129.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
30.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify116.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	152	473
1	385	408
2	992	406
3	3312	406
4	5001	406

prune127.0ms

Filtered

65 candidates to 41 candidates (63.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	63	5	68

Merged error: 0.5b

Counts

68 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
0.0b	(expm1 (expm1 (log1p (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))
0.1b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p` `expm1-udef`
1×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

1.0ms	(expm1 (log1p (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
1.0ms	(expm1 (expm1 (log1p (log1p (acos (/ (- 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)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(expm1 (log1p (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
269.0ms	(expm1 (expm1 (log1p (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))
31.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	153	543
1	391	426
2	998	420
3	3318	420
4	5001	420

prune345.0ms

Filtered

65 candidates to 44 candidates (67.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.5b

Counts

70 → 4

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b	(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)))

simplify95.0ms

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

prune29.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Merged error: 0.5b

Counts

17 → 5

regimes137.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2995×	body	2560	valid
675.0ms	2515×	body	1280	valid
298.0ms	8052×	body	80	nan
251.0ms	1265×	body	640	valid
88.0ms	615×	body	320	valid
41.0ms	392×	body	160	valid
12.0ms	218×	body	80	valid