Details

analyze796.0ms

Algorithm: search

sample80.0ms

Algorithm

intervals

Results

37.0ms	94×	body	2560	valid
25.0ms	93×	body	1280	valid
7.0ms	38×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	valid

simplify97.0ms

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

prune4.0ms

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: 0.3b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 5.0 (* v v)))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

3.0ms	(- 1.0 (* 5.0 (* v v)))
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)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune123.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	2	88

Merged error: 0.3b

Counts

88 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow v 2) (pow v 4))
0.0b	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.3b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-*r/` `associate--l+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `acos-asin` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+ (pow v 2) (pow v 4))
8.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
9.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series23.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (pow v 2) (pow v 4))
5.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
8.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
3.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	222	434
1	995	393
2	5001	386

prune114.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	2	71

Merged error: 0.3b

Counts

71 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
0.0b	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.3b	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`distribute-rgt-in` `sub-neg` `asin-acos` `flip3--` `distribute-lft-in` `diff-log` `associate-*r/` `associate--l+` `flip--` `difference-of-squares`
1×	`flip3-+` `times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

9.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
6.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
9.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
6.0ms	(- (/ PI 2) (asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
8.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
3.0ms	(asin (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	277	590
1	1121	553
2	5001	548

prune131.0ms

Filtered

50 candidates to 73 candidates (-46.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Merged error: 0.3b

Counts

75 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
38.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
39.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
53.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	117	1278
1	425	1112
2	2705	1044
3	5001	1031

prune205.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	82	5	87

Merged error: 0.2b

Counts

87 → 5

regimes264.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

end0.0ms

analyze783.0ms

Algorithm: search

sample2.3s

Algorithm

intervals

Results

1.2s	3003×	body	2560	valid
672.0ms	2539×	body	1280	valid
231.0ms	1216×	body	640	valid
85.0ms	616×	body	320	valid
42.0ms	434×	body	160	valid
11.0ms	192×	body	80	valid
0.0ms	8×	body	80	nan

Details

analyze796.0ms

sample80.0ms

simplify97.0ms

prune4.0ms

localize7.0ms

rewrite17.0ms

series16.0ms

simplify39.0ms

prune123.0ms

localize11.0ms

rewrite26.0ms

series23.0ms

simplify36.0ms

prune114.0ms

localize15.0ms

rewrite26.0ms

series22.0ms

simplify39.0ms

prune131.0ms

localize13.0ms

rewrite10.0ms

series170.0ms

simplify85.0ms

prune205.0ms

regimes264.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze783.0ms

sample2.3s

Profiling