Details

sample297.0ms

Algorithm: halfpoints

simplify58.0ms

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	121	7
4	206	7
5	410	7
6	1017	7
7	2074	7
8	5001	7

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize52.0ms

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))
57.8b	(- (exp x) (exp (- x)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
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 → 99

Calls

4 calls:

28.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms	(+ (exp x) (exp (- x)))
26.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
22.0ms	(+ (exp x) (exp (- x)))
80.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
35.0ms	(- (exp x) (exp (- x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	508	967
1	1773	853
2	5001	852

prune390.0ms

Filtered

111 candidates to 84 candidates (75.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`add-cbrt-cube`
10×	`times-frac`
9×	`add-log-exp` `unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`sum-log` `*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
5.0ms	(* 1/60 (pow x 5))
35.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
7.0ms	(* 1/3 (pow x 3))

series235.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
51.0ms	(* 1/60 (pow x 5))
89.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
39.0ms	(* 1/3 (pow x 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	465	842
1	1988	741
2	5002	741

prune486.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

42.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
49.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
28.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms	(/ 1 (sqrt 2.0))

series510.0ms

Counts

4 → 10

Calls

4 calls:

164.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
224.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
123.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	684	2589
1	3667	2213
2	5002	2104

prune767.0ms

Filtered

192 candidates to 112 candidates (58.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow x 3))
0.2b	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b	(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt 2.0))
0.4b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`times-frac`
41×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
25×	`add-exp-log` `associate-l`
22×	`add-cbrt-cube`
15×	`associate-r`
12×	`associate-/r*`
7×	`prod-exp` `unswap-sqr`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `cube-prod` `associate-/l*` `add-log-exp`
3×	`div-inv` `associate-/l/`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `pow-prod-down` `pow-exp` `flip-+`

Counts

4 → 144

Calls

4 calls:

6.0ms	(* 1/3 (pow x 3))
44.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
14.0ms	(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt 2.0))
28.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series660.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/3 (pow x 3))
154.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
344.0ms	(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt 2.0))
128.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	614	2017
1	3067	1782
2	5001	1760

prune632.0ms

Filtered

156 candidates to 103 candidates (66.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	19
1	35	19

end0.0ms

sample6.0s

Algorithm: halfpoints