Details

sample47.0ms

Algorithm

intervals

Results

25.0ms	255×	body	80	valid
2.0ms	5×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune14.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
51×	`prod-diff`
42×	`add-cube-cbrt`
23×	`cos-sum` `times-frac`
12×	`unpow-prod-down`
11×	`associate-+r+` `add-log-exp`
10×	`fma-def`
7×	`fma-neg` `div-inv`
5×	`pow1` `add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `pow-unpow`
2×	`diff-log` `sum-log` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `cos-diff` `pow-to-exp` `associate-+r-` `flip3--` `pow-pow` `flip3-+` `pow-exp` `flip--` `flip-+`

Counts

4 → 137

Calls

4 calls:

19.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
9.0ms	(- (/ (* K (+ m n)) 2.0) M)
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series559.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
61.0ms	(- (/ (* K (+ m n)) 2.0) M)
266.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	666	1925
1	1838	1487
2	5002	1476

prune497.0ms

Filtered

149 candidates to 92 candidates (61.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	143	6	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	6	150

Merged error: 1.4b

Counts

150 → 6

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
12×	`add-cube-cbrt` `unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
7×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `pow-unpow` `distribute-lft-out--`
2×	`expm1-log1p-u` `times-frac` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

2 → 60

Calls

2 calls:

18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series447.0ms

Counts

2 → 6

Calls

2 calls:

177.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify129.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	326	528
1	945	464
2	4380	448
3	5001	448

prune224.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 1.4b

Counts

72 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
33.6b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

series202.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
202.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify98.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 4 (27.0ms)

Iter	Nodes	Cost
0	77	281
1	144	253
2	316	247
3	854	247
4	3641	244
5	5002	244

prune269.0ms

Filtered

55 candidates to 45 candidates (81.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	54	7	61

Merged error: 1.4b

Counts

61 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))
1.0b	(cbrt (cbrt 2.0))
33.6b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
20×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1` `add-exp-log` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/3` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down`
1×	`cos-sum` `pow3` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt 2.0)
6.0ms	(* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))
2.0ms	(cbrt (cbrt 2.0))
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

series204.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))
0.0ms	(cbrt (cbrt 2.0))
203.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (* (cbrt 2.0) (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	156	693
1	422	634
2	1481	626
3	5002	609

prune378.0ms

Filtered

79 candidates to 62 candidates (78.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	79	7	86

Merged error: 1.4b

Counts

86 → 7

regimes246.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

799.0ms	8073×	body	80	valid
63.0ms	153×	body	640	valid
61.0ms	100×	body	1280	valid
36.0ms	118×	body	320	valid
11.0ms	55×	body	160	valid
4.0ms	5×	body	2560	valid