Details

sample267.0ms

Algorithm: halfpoints

simplify57.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.8b	(- (exp x) (exp (- x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
22×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 87

Calls

3 calls:

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

series175.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
80.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
35.0ms	(- (exp x) (exp (- x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	480	867
1	1672	765
2	5002	765

prune341.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

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

rewrite63.0ms

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:

9.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
5.0ms	(* 1/60 (pow x 5))
7.0ms	(* 1/3 (pow x 3))
39.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series236.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
46.0ms	(* 1/60 (pow x 5))
41.0ms	(* 1/3 (pow x 3))
89.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify58.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	465	830
1	1991	734
2	5002	734

prune503.0ms

Pruning

11 alts after pruning (10 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:

40.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
50.0ms	(* (/ 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))

series509.0ms

Counts

4 → 10

Calls

4 calls:

162.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
218.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
129.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify98.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	684	2590
1	3667	2213
2	5002	2104

prune790.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize68.0ms

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	(* (cbrt (/ (/ 1 2.0) (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 2.0) (sqrt 2.0))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

311×	`times-frac`
188×	`add-sqr-sqrt`
180×	`add-cube-cbrt` `*-un-lft-identity`
107×	`associate-l`
103×	`sqrt-prod`
82×	`cbrt-prod`
29×	`add-exp-log`
22×	`add-cbrt-cube`
17×	`div-inv`
16×	`associate-/l*`
15×	`pow1`
12×	`associate-/r*`
9×	`div-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv`
4×	`associate-r` `pow-prod-down` `associate-*l/` `add-log-exp` `pow-div`
3×	`associate-/l/` `unswap-sqr`
2×	`cbrt-div` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `inv-pow`
1×	`frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*r/` `flip-+`

Counts

4 → 306

Calls

4 calls:

44.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
209.0ms	(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
29.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
8.0ms	(/ (/ 1 2.0) (sqrt 2.0))

series813.0ms

Counts

4 → 10

Calls

4 calls:

154.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
535.0ms	(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
124.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ (/ 1 2.0) (sqrt 2.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1125	4318
1	4869	3959
2	5001	3959

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

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