Details

Time bar (total: 13.3s)

sample282.0ms

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: 43.5b

localize54.0ms

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))
58.6b
(- (exp x) (exp (- x)))

rewrite64.0ms

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:
25.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
5.0ms
(+ (exp x) (exp (- x)))
25.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms
(- (exp x) (exp (- x)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
23.0ms
(+ (exp x) (exp (- x)))
82.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
40.0ms
(- (exp x) (exp (- x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0508967
11773853
25001852

prune390.0ms

Filtered
111 candidates to 84 candidates (75.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp x) (exp (- 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))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
22×associate-*r*
21×*-un-lft-identity
19×add-exp-log add-cube-cbrt associate-*l*
13×add-cbrt-cube
10×times-frac
9×unswap-sqr
8×unpow-prod-down prod-exp
6×pow1 add-log-exp
4×cube-prod cbrt-unprod sqr-pow
3×*-commutative
2×pow-to-exp pow-exp
1×cbrt-undiv +-commutative cube-mult flip3-+ unpow3 div-exp pow-prod-down associate-*l/ sum-log flip-+ div-inv distribute-lft-out
Counts
4 → 100
Calls
4 calls:
5.0ms
(+ (exp x) (exp (- x)))
5.0ms
(* 1/60 (pow x 5))
6.0ms
(* 1/3 (pow x 3))
38.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series212.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (exp x) (exp (- x)))
48.0ms
(* 1/60 (pow x 5))
42.0ms
(* 1/3 (pow x 3))
93.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify60.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0493776
12065675
25002675

prune517.0ms

Filtered
112 candidates to 78 candidates (69.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

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))
0.3b
(* (/ 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))

rewrite123.0ms

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:
38.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
48.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
27.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms
(/ 1 (sqrt 2.0))

series634.0ms

Counts
4 → 10
Calls
4 calls:
153.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
220.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
260.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify96.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06842589
136672213
250022104

prune766.0ms

Filtered
192 candidates to 112 candidates (58.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (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 (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite244.0ms

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×add-log-exp
3×frac-2neg pow-prod-down associate-*l/ clear-num associate-/l/
2×inv-pow
1×frac-times flip3-+ associate-*r/ associate-*r* *-commutative flip-+
Counts
4 → 767
Calls
4 calls:
127.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
27.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
17.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms
(/ 1 (sqrt (sqrt 2.0)))

series342.0ms

Counts
4 → 8
Calls
4 calls:
219.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (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 (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify132.0ms

Algorithm
egg-herbie
Counts
775 → 775
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0173312573
1500111020

prune2.8s

Filtered
775 candidates to 350 candidates (45.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes98.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03519
13519

end0.0ms

sample5.9s

Algorithm
halfpoints