Details

sample131.0ms

Algorithm

intervals

Results

49.0ms	69×	body	1280	valid
32.0ms	60×	body	640	valid
20.0ms	193×	body	80	valid
10.0ms	29×	body	320	valid
2.0ms	9×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	48	13
1	161	13
2	944	13
3	5002	12

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 29.5b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (pow t 3.0) (sin k))
3.9b	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
6.5b	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
22.0b	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

50×	`frac-times`
42×	`associate-/l/`
31×	`associate-/l*`
27×	`clear-num`
26×	`frac-2neg`
21×	`associate-/r` `-commutative`
11×	`div-inv`
10×	`associate-l` `associate-*l/`
8×	`sqr-pow`
5×	`associate-*r/`
2×	`tan-quot` `associate-/r/`
1×	`associate-r` `un-div-inv`

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (pow t 3.0) (sin k))
6.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
14.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (pow t 3.0) (sin k))
327.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
71.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
839.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify89.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	640	986
1	3532	970
2	5001	969

prune386.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	12	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	89	13	102

Merged error: 20.9b

Counts

102 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (pow t 3.0) (sin k))
2.4b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
3.4b	(* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l)
18.7b	(/ (* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l) (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`associate-l`
20×	`times-frac` `div-inv`
16×	`distribute-neg-frac`
15×	`*-commutative`
13×	`associate-*l/`
12×	`neg-mul-1`
10×	`associate-/r*`
8×	`associate-/r/`
7×	`clear-num`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `frac-2neg` `associate-r` `associate-/l/`
5×	`associate-/l*`
4×	`tan-quot`
3×	`frac-times` `associate-*r/` `sqr-pow`
2×	`distribute-lft-neg-out`
1×	`distribute-frac-neg` `un-div-inv`

Counts

4 → 63

Calls

4 calls:

4.0ms	(* (pow t 3.0) (sin k))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
5.0ms	(* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l)
14.0ms	(/ (* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l) (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

series1.5s

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (pow t 3.0) (sin k))
108.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
348.0ms	(* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l)
825.0ms	(/ (* (- (/ 2.0 (* (pow t 3.0) (sin k)))) l) (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

simplify74.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	617	803
1	3015	772
2	5002	771

prune426.0ms

Filtered

75 candidates to 72 candidates (96.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	73	15	88

Merged error: 19.7b

Counts

88 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
2.4b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
8.2b	(/ (* (- (/ 2.0 (sin k))) l) (* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)))
15.9b	(* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`associate-l`
35×	`times-frac`
26×	`div-inv`
23×	`*-commutative`
22×	`associate-*l/`
16×	`neg-mul-1`
15×	`associate-r` `distribute-neg-frac`
12×	`tan-quot` `clear-num`
9×	`frac-times` `frac-2neg` `associate-*r/`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r/`
7×	`associate-/r*` `sqr-pow`
5×	`associate-/l*`
4×	`distribute-lft-neg-out`
3×	`un-div-inv` `associate-/l/`
1×	`distribute-frac-neg`

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
13.0ms	(/ (* (- (/ 2.0 (sin k))) l) (* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)))
8.0ms	(* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
108.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
498.0ms	(/ (* (- (/ 2.0 (sin k))) l) (* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)))
347.0ms	(* (* (- (tan k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

simplify91.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	773	1186
1	3559	1144
2	5001	1144

prune548.0ms

Filtered

104 candidates to 100 candidates (96.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 19.7b

Counts

119 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
2.4b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
8.2b	(/ (* (- (/ 2.0 (sin k))) l) (/ (* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)) (cos k)))
15.7b	(* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-l`
15×	`div-inv`
14×	`associate-/r/`
12×	`associate-/l*`
11×	`associate-*l/`
10×	`clear-num`
9×	`associate-*r/`
7×	`frac-2neg` `*-commutative` `associate-/l/`
5×	`neg-mul-1` `times-frac` `associate-r`
4×	`distribute-lft-neg-out`
3×	`un-div-inv` `distribute-neg-frac`
2×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
1×	`distribute-frac-neg` `associate-/r*`

Counts

4 → 54

Calls

4 calls:

4.0ms	(* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
2.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
12.0ms	(/ (* (- (/ 2.0 (sin k))) l) (/ (* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)) (cos k)))
7.0ms	(* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
109.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
477.0ms	(/ (* (- (/ 2.0 (sin k))) l) (/ (* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0)) (cos k)))
346.0ms	(* (* (- (sin k)) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)) (pow t 3.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	592	747
1	2604	721
2	5001	721

prune320.0ms

Filtered

66 candidates to 62 candidates (93.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	66	10	76

Merged error: 19.6b

Counts

76 → 10

regimes236.0ms

Accuracy

81.7% (0.9b remaining)

Error of 22.4b against oracle of 21.5b and baseline of 26.5b

bsearch191.0ms

Steps

Iters	Range		Point
11	-6.214793287635471e-105	-1.1569418235616243e-125	-1.3623379860796222e-108

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	35
1	85	35
2	105	35
3	108	35
4	109	35
5	109	35

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2070×	body	1280	valid
841.0ms	1700×	body	640	valid
657.0ms	5961×	body	80	valid
291.0ms	832×	body	320	valid
96.0ms	410×	body	160	valid