Details

sample97.0ms

Algorithm

intervals

Results

37.0ms	98×	body	2560	valid
20.0ms	80×	body	1280	valid
9.0ms	270×	body	80	nan
8.0ms	43×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	8×	body	80	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5002	7

prune3.0ms

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: 0.6b

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))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite15.0ms

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×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `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 → 63

Calls

3 calls:

7.0ms	(/ (- 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)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune200.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.6b

Counts

73 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.1b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-exp-log`
9×	`add-sqr-sqrt` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod`
4×	`exp-prod` `add-log-exp`
3×	`associate-l` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-pow`
1×	`acos-asin` `rem-log-exp` `associate-r` `*-commutative` `rem-exp-log` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

1.0ms	(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms	(exp (log (acos (/ (- 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)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
3.0ms	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify116.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	156	537
1	407	466
2	1036	448
3	3485	442
4	5001	442

prune166.0ms

Filtered

66 candidates to 40 candidates (60.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.6b

Counts

70 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
4×	`associate-/r*`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
33.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
25.0ms	(* 5.0 (* v v))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	409	840
1	1459	784
2	5001	780

prune265.0ms

Filtered

91 candidates to 69 candidates (75.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	90	5	95

Merged error: 0.6b

Counts

95 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- (* v v) 1.0))
0.0b	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
0.1b	(* 5.0 (* v v))
0.6b	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
26×	`times-frac`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-exp-log`
19×	`associate-r`
16×	`add-cbrt-cube`
12×	`pow1`
7×	`prod-exp` `difference-of-squares`
6×	`associate-l`
5×	`cbrt-unprod`
4×	`flip3--` `div-exp` `pow-prod-down` `associate-/r*` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-l/` `-commutative` `div-inv`
1×	`acos-asin` `pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 109

Calls

4 calls:

6.0ms	(/ 1 (- (* v v) 1.0))
12.0ms	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (- (* v v) 1.0))
80.0ms	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	465	890
1	2189	783
2	5001	748

prune254.0ms

Filtered

121 candidates to 77 candidates (63.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	121	5	126

Merged error: 0.6b

Counts

126 → 5

regimes157.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	3066×	body	2560	valid
624.0ms	2490×	body	1280	valid
277.0ms	7984×	body	80	nan
237.0ms	1275×	body	640	valid
76.0ms	565×	body	320	valid
41.0ms	414×	body	160	valid
12.0ms	190×	body	80	valid

Details

sample97.0ms

simplify98.0ms

prune3.0ms

localize7.0ms

rewrite15.0ms

series109.0ms

simplify38.0ms

prune200.0ms

localize12.0ms

rewrite11.0ms

series105.0ms

simplify116.0ms

prune166.0ms

localize10.0ms

rewrite22.0ms

series142.0ms

simplify44.0ms

prune265.0ms

localize8.0ms

rewrite31.0ms

series152.0ms

simplify61.0ms

prune254.0ms

regimes157.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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