Details

sample272.0ms

Algorithm: halfpoints

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	7
1	47	7
2	84	7
3	131	7
4	223	7
5	466	7
6	1123	7
7	2244	7
8	5002	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 44.7b

Counts

2 → 1

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.9b	(- (exp x) (exp (- x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`associate-l`
31×	`add-cube-cbrt`
29×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`fma-def` `fma-neg`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 122

Calls

4 calls:

13.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms	(+ (exp x) (exp (- x)))
11.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
21.0ms	(+ (exp x) (exp (- x)))
79.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
34.0ms	(- (exp x) (exp (- x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	574	1243
1	2008	1013
2	5002	1009

prune460.0ms

Filtered

134 candidates to 98 candidates (73.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	3	135

Merged error: 0.1b

Counts

135 → 3

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
29×	`associate-l`
23×	`times-frac`
22×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `unswap-sqr`
3×	`fma-def`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef`

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
10.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms	(+ (exp x) (exp (- x)))
7.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series225.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
60.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
21.0ms	(+ (exp x) (exp (- x)))
87.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	487	969
1	1911	846
2	5001	842

prune580.0ms

Filtered

110 candidates to 86 candidates (78.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 188

Calls

4 calls:

8.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
14.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
4.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
5.0ms	(/ 1 (sqrt 2.0))

series481.0ms

Counts

4 → 10

Calls

4 calls:

154.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
208.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
118.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	633	2261
1	3213	1931
2	5001	1821

prune838.0ms

Filtered

198 candidates to 118 candidates (59.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	3	198
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 0b

Counts

208 → 8

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

1128×	`sqrt-prod`
1116×	`times-frac`
592×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
79×	`add-exp-log`
49×	`add-cbrt-cube`
37×	`associate-/l*`
32×	`div-exp`
25×	`prod-exp`
24×	`associate-/r*`
23×	`pow1` `div-inv`
20×	`sqrt-pow1`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num`
2×	`inv-pow`
1×	`frac-times` `associate-r/` `associate-r` `-commutative` `associate-/l/`

Counts

4 → 773

Calls

4 calls:

50.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
4.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
20.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ 1 (sqrt (sqrt 2.0)))

series336.0ms

Counts

4 → 8

Calls

4 calls:

215.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
121.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

781 → 781

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1680	11806
1	5002	10141

prune2.9s

Filtered

781 candidates to 355 candidates (45.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	779	2	781
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	782	7	789

Merged error: 0b

Counts

789 → 7

regimes110.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	29	17

end0.0ms

sample6.0s

Algorithm: halfpoints