Details

sample105.0ms

Algorithm

intervals

Results

21.0ms	49×	body	1280	valid
19.0ms	310×	body	80	nan
12.0ms	186×	body	80	valid
11.0ms	15×	body	2560	valid
7.0ms	24×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify29.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 21.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.4b	(/ (* z t) 3.0)
26.9b	(cos (- y (/ (* z t) 3.0)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 306

Calls

4 calls:

8.0ms	(/ a (* b 3.0))
32.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
9.0ms	(/ (* z t) 3.0)
35.0ms	(cos (- y (/ (* z t) 3.0)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ a (* b 3.0))
115.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
28.0ms	(/ (* z t) 3.0)
43.0ms	(cos (- y (/ (* z t) 3.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	2212	8598
1	5001	7928

prune1.5s

Filtered

318 candidates to 191 candidates (60.1%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	287	31	318
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	31	319

Merged error: 15.1b

Counts

319 → 31

localize54.0ms

Local error

Found 4 expressions with local error:

26.6b	(sin (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
26.7b	(cos (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 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` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `sin-sum`

Counts

4 → 40

Calls

4 calls:

2.0ms	(sin (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
2.0ms	(cos (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

series1.4s

Counts

4 → 12

Calls

4 calls:

225.0ms	(sin (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
238.0ms	(cos (fma 1 y (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))))
485.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
476.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	141	983
1	381	842
2	1489	801
3	5001	743

prune658.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	43	9	52
Fresh	4	26	30
Picked	1	0	1
Done	0	0	0
Total	48	35	83

Merged error: 15.0b

Counts

83 → 35

localize61.0ms

Local error

Found 4 expressions with local error:

30.7b	(sin (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)))))
31.0b	(cos (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

rewrite524.0ms

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:

280.0ms	(sin (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)))))
241.0ms	(cos (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

132.0ms	(sin (- (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)))))
103.0ms	(cos (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
429.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
418.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	99	900
1	256	763
2	1142	725
3	5002	659

prune769.0ms

Filtered

52 candidates to 46 candidates (88.5%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	3	31	34
Picked	1	0	1
Done	0	0	0
Total	51	36	87

Merged error: 15.0b

Counts

87 → 36

localize71.0ms

Local error

Found 4 expressions with local error:

54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
54.6b	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 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`

Counts

4 → 40

Calls

4 calls:

1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
1.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

series1.7s

Counts

4 → 12

Calls

4 calls:

429.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
427.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
425.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))
434.0ms	(fma (- (/ (cbrt t) (sqrt 3.0))) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0)) (* (/ (cbrt t) (sqrt 3.0)) (/ (* z (* (cbrt t) (cbrt t))) (sqrt 3.0))))

simplify298.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	41	1100
1	116	928
2	538	864
3	4435	708
4	5001	708

prune568.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	2	33	35
Picked	1	0	1
Done	0	0	0
Total	51	37	88

Merged error: 14.9b

Counts

88 → 37

regimes5.1s

Accuracy

27.8% (3.2b remaining)

Error of 18.8b against oracle of 15.6b and baseline of 20.0b

bsearch6.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	101
1	85	101
2	91	101
3	93	101
4	93	101

end0.0ms

sample2.9s

Algorithm

intervals

Results

658.0ms	1597×	body	1280	valid
575.0ms	9303×	body	80	nan
366.0ms	5608×	body	80	valid
266.0ms	949×	body	640	valid
255.0ms	370×	body	2560	valid
86.0ms	418×	body	320	valid
33.0ms	220×	body	160	valid