Details

Time bar (total: 11.3s)

sample253.0ms

Algorithm
halfpoints

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0307
1477
2847
31217
42067
54107
610177
720747
850017

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.9b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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

series197.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (exp x) (exp (- x)))
61.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
80.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
34.0ms
(- (exp x) (exp (- x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0508967
11773853
25001852

prune384.0ms

Filtered
111 candidates to 84 candidates (75.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
0.0b
(* 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))

rewrite62.0ms

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))
6.0ms
(* 1/3 (pow x 3))
36.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series228.0ms

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))
34.0ms
(* 1/3 (pow x 3))
89.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify63.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0465830
11991734
25002734

prune493.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ (* 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:
41.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
46.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
31.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms
(/ 1 (sqrt 2.0))

series501.0ms

Counts
4 → 10
Calls
4 calls:
159.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
221.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
121.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06842589
136672213
250022104

prune781.0ms

Filtered
192 candidates to 112 candidates (58.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

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:
9.0ms
(* 1/3 (pow x 3))
39.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
41.0ms
(* (pow 2.0 (- 1/2)) (* (/ (+ (* 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))

series669.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* 1/3 (pow x 3))
151.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
365.0ms
(* (pow 2.0 (- 1/2)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
119.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify93.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06832100
133511868
250011864

prune701.0ms

Filtered
159 candidates to 102 candidates (64.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03519
13519

end0.0ms

sample6.0s

Algorithm
halfpoints