Details

Time bar (total: 14.4s)

sample310.0ms

Algorithm
halfpoints

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0307
1477
2847
31217
42067
54107
610177
720747
850017

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.2b

localize36.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.9b
(- (exp x) (exp (- x)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×*-un-lft-identity
19×associate-*l*
16×times-frac
12×add-cube-cbrt
7×add-exp-log add-cbrt-cube
4×pow1 distribute-lft-out-- add-log-exp difference-of-squares
3×associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv sub-neg flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-- div-inv
Counts
2 → 52
Calls
2 calls:
28.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms
(- (exp x) (exp (- x)))

series20.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
4.0ms
(- (exp x) (exp (- x)))

simplify106.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0293506
1893449
23855448
35001448

prune388.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

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))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
22×associate-*r*
19×associate-*l*
18×add-exp-log add-cube-cbrt *-un-lft-identity
12×add-cbrt-cube
10×times-frac
9×unswap-sqr
8×unpow-prod-down prod-exp
5×pow1
4×cube-prod cbrt-unprod sqr-pow
3×*-commutative add-log-exp
2×pow-to-exp pow-exp
1×cbrt-undiv cube-mult unpow3 div-exp pow-prod-down associate-*l/ div-inv
Counts
3 → 88
Calls
3 calls:
5.0ms
(* 1/60 (pow x 5))
36.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
7.0ms
(* 1/3 (pow x 3))

series21.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(* 1/60 (pow x 5))
16.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
3.0ms
(* 1/3 (pow x 3))

simplify47.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0399664
11676581
25002581

prune724.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

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))
0.3b
(* (/ 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))

rewrite130.0ms

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)))
29.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms
(/ 1 (sqrt 2.0))

series61.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
29.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
9.0ms
(/ (+ (* 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 (69.0ms)

IterNodesCost
06842589
136672213
250022104

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize39.0ms

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
(* (pow 2.0 (- 1/2)) (* (/ (+ (* 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))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×add-exp-log
39×add-cube-cbrt *-un-lft-identity
38×times-frac
32×associate-*l*
22×sqrt-prod add-cbrt-cube
20×prod-exp
16×associate-*r*
8×cbrt-unprod
7×unpow-prod-down unswap-sqr
6×pow1 associate-*l/ associate-/r*
5×div-exp
4×pow-to-exp cube-prod pow-exp add-log-exp
3×cbrt-undiv *-commutative associate-/l* sqr-pow
2×neg-sub0 frac-times pow-neg div-inv associate-/l/ pow-sub
1×cube-mult frac-2neg flip3-+ unpow3 associate-*r/ pow-prod-down clear-num flip-+
Counts
4 → 147
Calls
4 calls:
7.0ms
(* 1/3 (pow x 3))
40.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
42.0ms
(* (pow 2.0 (- 1/2)) (* (/ (+ (* 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))

series67.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 1/3 (pow x 3))
23.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
33.0ms
(* (pow 2.0 (- 1/2)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
8.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify95.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06832107
133511871
250011867

prune1.6s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes202.0ms

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)

IterNodesCost
02410
12410

end0.0ms

sample8.5s

Algorithm
halfpoints