Details

sample134.0ms

Algorithm

intervals

Results

30.0ms	58×	body	1280	valid
25.0ms	291×	body	80	nan
13.0ms	165×	body	80	valid
12.0ms	14×	body	2560	valid
12.0ms	34×	body	640	valid
4.0ms	12×	body	320	valid
2.0ms	10×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	10
1	55	10
2	76	10
3	89	10
4	92	10
5	92	10

prune3.0ms

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: 22.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* z t) 3.0)
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.5b	(/ a (* b 3.0))
23.9b	(cos (- y (/ (* z t) 3.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `frac-2neg` `clear-num` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

5.0ms	(/ (* z t) 3.0)
10.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
7.0ms	(/ a (* b 3.0))
9.0ms	(cos (- y (/ (* z t) 3.0)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (* z t) 3.0)
123.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
27.0ms	(/ a (* b 3.0))
41.0ms	(cos (- y (/ (* z t) 3.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	507
1	1689	429
2	5001	426

prune318.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	62	22	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	22	85

Merged error: 17.9b

Counts

85 → 22

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
0.5b	(/ a (* b 3.0))
26.3b	(sin (/ (* z t) 3.0))
26.5b	(cos (/ (* z t) 3.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-r` `pow-prod-down` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `clear-num` `associate-/r` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 58

Calls

4 calls:

10.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
4.0ms	(/ a (* b 3.0))
2.0ms	(sin (/ (* z t) 3.0))
2.0ms	(cos (/ (* z t) 3.0))

series242.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
18.0ms	(/ a (* b 3.0))
15.0ms	(sin (/ (* z t) 3.0))
13.0ms	(cos (/ (* z t) 3.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	433	695
1	1951	580
2	5001	577

prune403.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	6	15	21
Picked	1	0	1
Done	0	0	0
Total	64	28	92

Merged error: 17.8b

Counts

92 → 28

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
0.5b	(/ a (* b 3.0))
26.3b	(sin (/ (* z t) 3.0))
26.5b	(cos (* 0.3333333333333333 (* t z)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-r` `pow-prod-down` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `clear-num` `associate-/r` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 58

Calls

4 calls:

14.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
5.0ms	(/ a (* b 3.0))
2.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
18.0ms	(/ a (* b 3.0))
15.0ms	(sin (/ (* z t) 3.0))
10.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	437	695
1	1967	580
2	5001	577

prune439.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	8	19	27
Picked	1	0	1
Done	0	0	0
Total	70	28	98

Merged error: 17.7b

Counts

98 → 28

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
0.3b	(* (/ 1 b) (/ a 3.0))
26.3b	(sin (/ (* z t) 3.0))
26.5b	(cos (* 0.3333333333333333 (* t z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
31×	`add-exp-log`
25×	`times-frac`
21×	`*-un-lft-identity` `add-cbrt-cube`
19×	`add-cube-cbrt`
16×	`associate-r`
14×	`associate-l`
11×	`pow1` `prod-exp`
8×	`div-exp`
7×	`cbrt-unprod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `associate-*r/` `pow-prod-down` `add-log-exp`
2×	`rec-exp` `1-exp` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `associate-*l/` `frac-add` `cos-mult` `flip-+` `sin-mult`

Counts

4 → 93

Calls

4 calls:

10.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
10.0ms	(* (/ 1 b) (/ a 3.0))
2.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
16.0ms	(* (/ 1 b) (/ a 3.0))
15.0ms	(sin (/ (* z t) 3.0))
10.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify84.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	662	906
1	3129	756
2	5001	750

prune487.0ms

Filtered

105 candidates to 74 candidates (70.5%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	27	27
Picked	0	1	1
Done	0	0	0
Total	105	28	133

Merged error: 17.7b

Counts

133 → 28

regimes3.1s

Accuracy

63.1% (1.4b remaining)

Error of 18.3b against oracle of 16.9b and baseline of 20.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	31
1	56	31
2	56	31

end0.0ms

sample2.8s

Algorithm

intervals

Results

644.0ms	1642×	body	1280	valid
542.0ms	9321×	body	80	nan
347.0ms	5624×	body	80	valid
263.0ms	962×	body	640	valid
229.0ms	350×	body	2560	valid
86.0ms	421×	body	320	valid
31.0ms	202×	body	160	valid