Details

sample138.0ms

Algorithm

intervals

Results

32.0ms	302×	body	80	nan
27.0ms	46×	body	1280	valid
19.0ms	185×	body	80	valid
14.0ms	32×	body	640	valid
12.0ms	13×	body	2560	valid
3.0ms	10×	body	320	valid
2.0ms	10×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	58	10
2	82	10
3	99	10
4	107	10
5	109	10
6	109	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(/ a (* b 3.0))
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
23.7b	(cos (- y (/ (* z t) 3.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`prod-diff`
19×	`add-exp-log` `add-cbrt-cube`
15×	`times-frac`
9×	`pow1`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 101

Calls

4 calls:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
15.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
16.0ms	(cos (- y (/ (* z t) 3.0)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* z t) 3.0)
20.0ms	(/ a (* b 3.0))
95.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
34.0ms	(cos (- y (/ (* z t) 3.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	685	1511
1	2361	1261
2	5001	1258

prune456.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 15.5b

localize40.0ms

Local error

Found 4 expressions with local error:

23.5b	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
24.0b	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite3.0ms

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`
1×	`cos-sum` `sin-sum`

Counts

4 → 40

Calls

4 calls:

1.0ms	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
1.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
179.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
188.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
187.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	124	593
1	303	510
2	1138	489
3	5001	459

prune548.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 15.4b

localize49.0ms

Local error

Found 4 expressions with local error:

23.5b	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
24.0b	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite3.0ms

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`
1×	`cos-sum` `sin-sum`

Counts

4 → 40

Calls

4 calls:

1.0ms	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
1.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
183.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
187.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
189.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	128	579
1	307	498
2	1145	476
3	5001	446

prune644.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 15.4b

localize49.0ms

Local error

Found 4 expressions with local error:

23.5b	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
24.0b	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
52.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite3.0ms

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`
1×	`cos-sum` `sin-sum`

Counts

4 → 40

Calls

4 calls:

1.0ms	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
1.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
0.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sin (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
185.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
194.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
192.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	128	579
1	307	498
2	1145	476
3	5001	446

prune493.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 15.4b

regimes4.2s

Accuracy

60.6% (1.7b remaining)

Error of 17.2b against oracle of 15.5b and baseline of 19.9b

bsearch4.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	71
1	82	71
2	82	71

end0.0ms

sample4.1s

Algorithm

intervals

Results

939.0ms	1542×	body	1280	valid
926.0ms	9328×	body	80	nan
606.0ms	5739×	body	80	valid
421.0ms	969×	body	640	valid
321.0ms	338×	body	2560	valid
140.0ms	432×	body	320	valid
49.0ms	215×	body	160	valid