Details

sample105.0ms

Algorithm

intervals

Results

18.0ms	303×	body	80	nan
16.0ms	46×	body	1280	valid
13.0ms	202×	body	80	valid
7.0ms	31×	body	640	valid
7.0ms	12×	body	2560	valid
2.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify13.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(/ (* z t) 3.0)
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
21.7b	(cos (- y (/ (* z t) 3.0)))

rewrite76.0ms

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:

7.0ms	(/ a (* b 3.0))
9.0ms	(/ (* z t) 3.0)
31.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
25.0ms	(cos (- y (/ (* z t) 3.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ a (* b 3.0))
15.0ms	(/ (* z t) 3.0)
83.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
33.0ms	(cos (- y (/ (* z t) 3.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (51.0ms)

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

prune438.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.8b

localize37.0ms

Local error

Found 4 expressions with local error:

21.5b	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
21.7b	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite6.0ms

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:

2.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
2.0ms	(sin (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))))

series640.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
151.0ms	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
166.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
161.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	124	593
1	305	510
2	1140	489
3	5002	459

prune549.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 14.7b

localize45.0ms

Local error

Found 4 expressions with local error:

21.4b	(cos (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
21.7b	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite6.0ms

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:

2.0ms	(cos (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
2.0ms	(sin (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))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cos (fma 1 y (- (/ (* t z) (pow (sqrt 3.0) 2)))))
148.0ms	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
160.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
160.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	128	579
1	309	498
2	1147	476
3	5001	446

prune645.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 14.6b

localize59.0ms

Local error

Found 4 expressions with local error:

25.5b	(sin (- (/ (* t z) (pow (sqrt 3.0) 2))))
25.5b	(cos (/ (* t z) (pow (sqrt 3.0) 2)))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.5b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite32.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`neg-sub0` `sin-neg` `sin-diff`

Counts

4 → 40

Calls

4 calls:

17.0ms	(sin (- (/ (* t z) (pow (sqrt 3.0) 2))))
8.0ms	(cos (/ (* t z) (pow (sqrt 3.0) 2)))
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))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sin (- (/ (* t z) (pow (sqrt 3.0) 2))))
68.0ms	(cos (/ (* t z) (pow (sqrt 3.0) 2)))
164.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
160.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	84	494
1	194	415
2	908	393
3	5002	334

prune516.0ms

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 14.6b

regimes4.3s

Accuracy

54.5% (2.0b remaining)

Error of 18.4b against oracle of 16.4b and baseline of 20.8b

bsearch4.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	76
1	94	76
2	94	76

end0.0ms

sample3.0s

Algorithm

intervals

Results

597.0ms	1622×	body	1280	valid
555.0ms	8966×	body	80	nan
312.0ms	5573×	body	80	valid
249.0ms	994×	body	640	valid
224.0ms	360×	body	2560	valid
76.0ms	433×	body	320	valid
24.0ms	193×	body	160	valid