Details

sample90.0ms

Algorithm

intervals

Results

17.0ms	45×	body	1280	valid
17.0ms	265×	body	80	nan
11.0ms	188×	body	80	valid
7.0ms	10×	body	2560	valid
6.0ms	23×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 19.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.4b	(/ (* z t) 3.0)
23.6b	(cos (- y (/ (* z t) 3.0)))

rewrite37.0ms

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	(/ a (* b 3.0))
14.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
3.0ms	(/ (* z t) 3.0)
13.0ms	(cos (- y (/ (* z t) 3.0)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ a (* b 3.0))
94.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
17.0ms	(/ (* z t) 3.0)
37.0ms	(cos (- y (/ (* z t) 3.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (54.0ms)

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

prune427.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 14.6b

localize34.0ms

Local error

Found 4 expressions with local error:

23.5b	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
23.8b	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.1b	(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	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
1.0ms	(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))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cos (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
166.0ms	(sin (fma 1 y (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))))
174.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
171.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (38.0ms)

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

prune504.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 14.4b

localize48.0ms

Local error

Found 4 expressions with local error:

26.7b	(cos (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
26.8b	(sin (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0)))))
53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.1b	(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` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`neg-sub0` `sin-neg` `sin-diff`

Counts

4 → 40

Calls

4 calls:

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

series544.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cos (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
108.0ms	(sin (- (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0)))))
181.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
179.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify40.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	90	520
1	205	435
2	977	417
3	5002	360

prune639.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 14.3b

localize57.0ms

Local error

Found 4 expressions with local error:

53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
53.1b	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

rewrite2.0ms

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`

Counts

4 → 40

Calls

4 calls:

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))))
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))))

series731.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
182.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
183.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))
181.0ms	(fma (- (/ t (sqrt 3.0))) (/ z (sqrt 3.0)) (* (/ t (sqrt 3.0)) (/ z (sqrt 3.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (78.0ms)

Iter	Nodes	Cost
0	33	600
1	79	508
2	312	492
3	1866	396
4	5001	144

prune498.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 14.3b

regimes4.1s

Accuracy

41.4% (2.5b remaining)

Error of 18.8b against oracle of 16.4b and baseline of 20.6b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	101
1	80	101
2	80	101

end0.0ms

sample3.0s

Algorithm

intervals

Results

674.0ms	1631×	body	1280	valid
609.0ms	8975×	body	80	nan
353.0ms	5592×	body	80	valid
278.0ms	976×	body	640	valid
273.0ms	397×	body	2560	valid
82.0ms	389×	body	320	valid
33.0ms	209×	body	160	valid