Details

sample42.0ms

Algorithm

intervals

Results

20.0ms	258×	body	80	valid
2.0ms	5×	body	1280	valid
2.0ms	5×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `prod-diff`
36×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`pow1` `add-exp-log` `fma-neg` `div-inv`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

9.0ms	(- (/ (* K (+ m n)) 2.0) M)
6.0ms	(* K (+ m n))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series401.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ (* K (+ m n)) 2.0) M)
24.0ms	(* K (+ m n))
261.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify62.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	612	1660
1	1907	1270
2	5003	1268

prune449.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

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)

rewrite34.0ms

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:

22.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series440.0ms

Counts

2 → 6

Calls

2 calls:

176.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
264.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify123.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (27.0ms)

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

prune231.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
35.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod`
9×	`times-frac`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 81

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
22.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series482.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (+ m n))
130.0ms	(cbrt (+ m n))
126.0ms	(cbrt (+ m n))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify88.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	427	1747
1	906	1467
2	3154	1458
3	5001	1308

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
2.2b	(exp (log (cbrt (+ m n))))
18.9b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
23×	`cos-sum`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`prod-diff`
12×	`cbrt-prod`
9×	`times-frac`
7×	`log-prod` `exp-sum`
6×	`cbrt-div`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv` `distribute-lft-out`
2×	`log-div` `exp-diff` `log-pow`
1×	`cos-diff` `sub-neg` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
5.0ms	(exp (log (cbrt (+ m n))))
21.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

series483.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ m n))
125.0ms	(cbrt (+ m n))
132.0ms	(exp (log (cbrt (+ m n))))
101.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (exp (log (cbrt (+ m n))))) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	474	1937
1	996	1641
2	3298	1628
3	5001	1446

prune451.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes167.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

660.0ms	8088×	body	80	valid
64.0ms	128×	body	1280	valid
57.0ms	154×	body	640	valid
30.0ms	118×	body	320	valid
14.0ms	57×	body	160	valid
3.0ms	4×	body	2560	valid