Details

sample96.0ms

Algorithm

intervals

Results

41.0ms	103×	body	2560	valid
24.0ms	85×	body	1280	valid
9.0ms	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

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	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

localize10.0ms

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)))

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×	`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)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (33.0ms)

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

prune138.0ms

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: 0.7b

Counts

73 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow v 2) (pow v 4))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.7b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

7.0ms	(+ (pow v 2) (pow v 4))
13.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series166.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(+ (pow v 2) (pow v 4))
90.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify156.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	177	315
1	834	276
2	4136	273
3	5002	273

prune97.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	53	3	56

Merged error: 0.7b

Counts

56 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
0.7b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

1.0ms	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
10.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
6.0ms	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series184.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
90.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
5.0ms	(exp (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	193	551
1	815	484
2	3988	468
3	5002	462

prune152.0ms

Filtered

70 candidates to 43 candidates (61.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.7b

Counts

73 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b	(pow (exp (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))) (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))
0.7b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
0.7b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`pow1`
8×	`pow-pow` `sqrt-prod`
7×	`pow-unpow` `exp-prod`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `associate-l`
2×	`acos-asin` `associate-*r/` `log-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

14.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
5.0ms	(pow (exp (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))) (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series478.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
378.0ms	(pow (exp (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))) (sqrt (log (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	234	897
1	1023	823
2	5001	822

prune230.0ms

Filtered

79 candidates to 51 candidates (64.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Merged error: 0.6b

Counts

84 → 6

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	21	39

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2973×	body	2560	valid
693.0ms	2524×	body	1280	valid
309.0ms	8042×	body	80	nan
258.0ms	1263×	body	640	valid
93.0ms	629×	body	320	valid
43.0ms	413×	body	160	valid
12.0ms	198×	body	80	valid