Details

sample41.0ms

Algorithm

intervals

Results

21.0ms	262×	body	80	valid
2.0ms	3×	body	1280	valid
1.0ms	3×	body	320	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid

simplify51.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite46.0ms

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)
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
6.0ms	(* K (+ m n))
16.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series424.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (/ (* K (+ m n)) 2.0) M)
270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
39.0ms	(* K (+ m n))
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

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

prune485.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 79

Calls

3 calls:

18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
22.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series572.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
115.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
273.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	406	746
1	1310	664
2	5001	642

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (* K (+ m n)))
15.6b	(cbrt (* K (+ m n)))
15.6b	(cbrt (* K (+ m n)))
34.8b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
13.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series390.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (* K (+ m n)))
108.0ms	(cbrt (* K (+ m n)))
113.0ms	(cbrt (* K (+ m n)))
56.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	426	1888
1	786	1586
2	1878	1562
3	5002	1391

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize45.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (* K (+ m n)))
15.6b	(cbrt (* K (+ m n)))
34.6b	(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))
35.0b	(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `cbrt-div` `-un-lft-identity` `associate-r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
2.0ms	(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))
2.0ms	(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))

series1.5s

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* K (+ m n)))
105.0ms	(cbrt (* K (+ m n)))
567.0ms	(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))
747.0ms	(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (* (cbrt 2.0) (cbrt 2.0))) (/ (cbrt (* K (+ m n))) (cbrt 2.0)) (- (* M 1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	304	910
1	719	813
2	1946	797
3	5001	795

prune583.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes223.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

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

676.0ms	8074×	body	80	valid
67.0ms	133×	body	1280	valid
49.0ms	139×	body	640	valid
29.0ms	88×	body	320	valid
14.0ms	78×	body	160	valid
2.0ms	2×	body	2560	valid