Details

sample114.0ms

Algorithm

intervals

Results

26.0ms	61×	body	1280	valid
25.0ms	300×	body	80	nan
12.0ms	175×	body	80	valid
8.0ms	26×	body	640	valid
7.0ms	10×	body	2560	valid
3.0ms	15×	body	320	valid
1.0ms	4×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 21.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(/ (* z t) 3.0)
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
25.6b	(cos (- y (/ (* z t) 3.0)))

rewrite46.0ms

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))
4.0ms	(/ (* z t) 3.0)
19.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
16.0ms	(cos (- y (/ (* z t) 3.0)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ a (* b 3.0))
19.0ms	(/ (* z t) 3.0)
105.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
39.0ms	(cos (- y (/ (* z t) 3.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (64.0ms)

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

prune508.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 16.1b

localize42.0ms

Local error

Found 4 expressions with local error:

25.5b	(sin (fma 1 y (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))))
25.9b	(cos (fma 1 y (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

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`
1×	`cos-sum` `sin-sum`

Counts

4 → 40

Calls

4 calls:

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

series718.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sin (fma 1 y (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))))
123.0ms	(cos (fma 1 y (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))))
245.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
240.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

simplify228.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (220.0ms)

Iter	Nodes	Cost
0	110	733
1	261	629
2	892	609
3	4929	553
4	5001	517

prune615.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 15.9b

localize51.0ms

Local error

Found 4 expressions with local error:

29.2b	(sin (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0))))))
29.5b	(cos (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

rewrite7.0ms

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:

3.0ms	(sin (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0))))))
2.0ms	(cos (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
0.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
0.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sin (- (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0))))))
73.0ms	(cos (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
246.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
250.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

simplify216.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (209.0ms)

Iter	Nodes	Cost
0	91	661
1	206	562
2	718	542
3	3947	486
4	5001	450

prune739.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 15.9b

localize62.0ms

Local error

Found 4 expressions with local error:

52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
52.3b	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 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 (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
0.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
0.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
0.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

series998.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
246.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
244.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))
255.0ms	(fma (- (/ t (cbrt 3.0))) (/ z (* (cbrt 3.0) (cbrt 3.0))) (* (/ t (cbrt 3.0)) (/ z (* (cbrt 3.0) (cbrt 3.0)))))

simplify157.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (151.0ms)

Iter	Nodes	Cost
0	36	800
1	101	676
2	470	636
3	2972	524
4	5001	184

prune570.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 15.8b

regimes5.0s

Accuracy

31.3% (2.9b remaining)

Error of 18.9b against oracle of 16.0b and baseline of 20.2b

bsearch223.0ms

Steps

Iters	Range		Point
7	2.051813963975042e-16	1.4211274386154874e-14	1.004573058588543e-15
6	-2.9166015123382445e-49	-4.20352456416865e-50	-2.5871529893740023e-49

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	116
1	91	116
2	91	116

end0.0ms

sample3.0s

Algorithm

intervals

Results

674.0ms	1595×	body	1280	valid
628.0ms	9052×	body	80	nan
359.0ms	5611×	body	80	valid
284.0ms	960×	body	640	valid
277.0ms	403×	body	2560	valid
83.0ms	398×	body	320	valid
27.0ms	182×	body	160	valid