Details

sample485.0ms

Algorithm

intervals

Results

416.0ms	239×	body	10240	exit
27.0ms	261×	body	80	valid
2.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid

simplify50.0ms

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: 14.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
32.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

178×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
141×	`prod-diff`
123×	`exp-sum`
71×	`add-cube-cbrt`
66×	`unpow-prod-down`
52×	`distribute-rgt-neg-in`
50×	`distribute-lft-neg-in`
47×	`difference-of-squares`
41×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
15×	`add-log-exp`
11×	`sqr-pow`
8×	`exp-prod`
7×	`pow1` `add-exp-log`
6×	`diff-log` `add-cbrt-cube`
5×	`neg-mul-1` `rem-exp-log`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `div-inv`
2×	`sub-neg` `associate-*r/` `neg-log`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 226

Calls

4 calls:

9.0ms	(* K (+ m n))
30.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series455.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* K (+ m n))
258.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
116.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify98.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	1015	6007
1	2825	4853
2	5003	4363

prune551.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

330×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
249×	`prod-diff`
138×	`unpow-prod-down`
123×	`exp-sum`
115×	`add-cube-cbrt`
114×	`distribute-rgt-neg-in`
110×	`distribute-lft-neg-in`
96×	`difference-of-squares`
83×	`distribute-lft-out--`
24×	`fma-neg` `add-log-exp`
23×	`times-frac` `sqr-pow`
12×	`diff-log`
11×	`neg-mul-1` `associate--r+`
8×	`exp-prod`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `neg-log`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `exp-diff` `pow-exp` `flip--`

Counts

3 → 347

Calls

3 calls:

655.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
32.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series558.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
257.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
121.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	783	9869
1	2227	7499
2	5001	5146

prune500.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
31.8b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `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`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
1.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series412.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
207.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
205.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify127.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	162	538
1	381	481
2	991	472
3	3226	466
4	5001	466

prune463.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

31.8b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
32.0b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

1.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
210.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
206.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
207.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify56.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	108	754
1	251	653
2	596	652
3	1348	652
4	5002	652

prune499.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

regimes224.0ms

Accuracy

0% (0.3b 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	21	10
1	23	10
2	23	10

end0.0ms

sample16.0s

Algorithm

intervals

Results

14.4s	8258×	body	10240	exit
890.0ms	8111×	body	80	valid
70.0ms	107×	body	1280	valid
63.0ms	154×	body	640	valid
28.0ms	92×	body	320	valid
10.0ms	50×	body	160	valid
4.0ms	4×	body	2560	valid