Details

sample104.0ms

Algorithm

intervals

Results

22.0ms	53×	body	1280	valid
20.0ms	330×	body	80	nan
11.0ms	172×	body	80	valid
9.0ms	13×	body	2560	valid
7.0ms	25×	body	640	valid
4.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify20.0ms

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

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: 19.7b

Counts

2 → 1

localize23.0ms

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))))
24.6b	(cos (- y (/ (* z t) 3.0)))

rewrite35.0ms

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:

5.0ms	(/ (* z t) 3.0)
5.0ms	(/ a (* b 3.0))
11.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
10.0ms	(cos (- y (/ (* z t) 3.0)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* z t) 3.0)
23.0ms	(/ a (* b 3.0))
106.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
38.0ms	(cos (- y (/ (* z t) 3.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (65.0ms)

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

prune449.0ms

Filtered

113 candidates to 72 candidates (63.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	94	19	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	19	114

Merged error: 15.9b

Counts

114 → 19

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 (sqrt x)) (- (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (- (/ (* z t) 3.0))))))
0.2b	(* (sin y) (sin (- (/ (* z t) 3.0))))
29.4b	(cos (/ (* z t) 3.0))
29.8b	(sin (- (/ (* z t) 3.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `sin-mult`
2×	`sub-neg` `prod-diff` `sin-neg` `cos-mult` `*-commutative`
1×	`neg-sub0` `flip3--` `sin-diff` `distribute-rgt-neg-out` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

11.0ms	(* (* 2.0 (sqrt x)) (- (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (- (/ (* z t) 3.0))))))
6.0ms	(* (sin y) (sin (- (/ (* z t) 3.0))))
2.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (- (/ (* z t) 3.0)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (* 2.0 (sqrt x)) (- (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (- (/ (* z t) 3.0))))))
57.0ms	(* (sin y) (sin (- (/ (* z t) 3.0))))
11.0ms	(cos (/ (* z t) 3.0))
22.0ms	(sin (- (/ (* z t) 3.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	417	1026
1	1822	885
2	5001	868

prune517.0ms

Filtered

84 candidates to 64 candidates (76.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	81	22	103

Merged error: 15.8b

Counts

103 → 22

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (- (/ (* z t) 3.0))))
0.3b	(log (exp (cos (/ (* z t) 3.0))))
29.4b	(cos (/ (* z t) 3.0))
29.8b	(sin (- (/ (* z t) 3.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod` `associate-r` `associate-l`
2×	`sin-neg`
1×	`neg-sub0` `rem-log-exp` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

6.0ms	(* (sin y) (sin (- (/ (* z t) 3.0))))
4.0ms	(log (exp (cos (/ (* z t) 3.0))))
2.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (- (/ (* z t) 3.0)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin y) (sin (- (/ (* z t) 3.0))))
11.0ms	(log (exp (cos (/ (* z t) 3.0))))
11.0ms	(cos (/ (* z t) 3.0))
22.0ms	(sin (- (/ (* z t) 3.0)))

simplify108.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	157	437
1	426	381
2	1126	381
3	2909	381
4	5001	381

prune552.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	71	22	93

Merged error: 15.8b

Counts

93 → 22

localize40.0ms

Local error

Found 4 expressions with local error:

29.4b	(cos (/ (* z t) 3.0))
29.4b	(cos (/ (* z t) 3.0))
29.4b	(cos (/ (* z t) 3.0))
29.8b	(sin (- (/ (* z t) 3.0)))

rewrite11.0ms

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`
1×	`neg-sub0` `sin-neg` `sin-diff`

Counts

4 → 38

Calls

4 calls:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(cos (/ (* z t) 3.0))
11.0ms	(cos (/ (* z t) 3.0))
11.0ms	(cos (/ (* z t) 3.0))
22.0ms	(sin (- (/ (* z t) 3.0)))

simplify372.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	63	239
1	122	208
2	244	208
3	478	208
4	2847	208
5	5002	208

prune346.0ms

Filtered

50 candidates to 46 candidates (92.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	49	23	72

Merged error: 15.8b

Counts

72 → 23

regimes2.7s

Accuracy

59% (1.6b remaining)

Error of 17.6b against oracle of 16.0b and baseline of 19.9b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	42
1	67	42
2	67	42

end0.0ms

sample3.0s

Algorithm

intervals

Results

682.0ms	1575×	body	1280	valid
609.0ms	8978×	body	80	nan
377.0ms	5580×	body	80	valid
272.0ms	908×	body	640	valid
264.0ms	371×	body	2560	valid
94.0ms	437×	body	320	valid
32.0ms	208×	body	160	valid