Details

Time bar (total: 6.2s)

sample60.0ms

Algorithm
intervals
Results
23.0ms42×body1280valid
15.0ms52×body640valid
9.0ms140×body80valid
3.0ms15×body320valid
1.0ms7×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0209
1439
2939
31749
42699
52889
62889

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b
(* (/ 8.0 3.0) (sin (* x 0.5)))
16.6b
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log add-cbrt-cube
19×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*l*
13×times-frac
12×prod-exp cbrt-unprod
10×pow1
7×cbrt-undiv div-exp
6×associate-*r*
5×associate-*l/
4×pow-prod-down
3×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/l/ associate-/l*
Counts
3 → 85
Calls
3 calls:
20.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series192.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
46.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))
88.0ms
(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify67.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0412862
12127656
25001637

prune272.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b
(/ (sin x) (sin (* 0.5 x)))
0.4b
(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
50×times-frac
38×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
31×add-exp-log add-cbrt-cube
16×associate-/r*
13×cbrt-undiv div-exp associate-*l*
6×prod-exp cbrt-unprod
5×pow1 div-inv
4×associate-/l*
3×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×frac-2neg associate-*l/ clear-num unswap-sqr
1×pow-prod-down associate-/r/ *-commutative associate-/l/
Counts
3 → 116
Calls
3 calls:
11.0ms
(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms
(/ (sin x) (sin (* 0.5 x)))
10.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

series179.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
50.0ms
(/ (sin x) (sin (* 0.5 x)))
39.0ms
(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify73.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05501204
127271016
25001992

prune390.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
0.1b
(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
0.2b
(/ (sin x) (sin (* 0.5 x)))
0.2b
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
59×times-frac
50×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
34×add-exp-log add-cbrt-cube
32×associate-*l*
28×sqrt-prod
16×associate-/r*
11×pow1
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×sqrt-div
7×associate-*l/
6×div-inv
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*r/ clear-num *-commutative
1×associate-/r/
Counts
4 → 156
Calls
4 calls:
13.0ms
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
31.0ms
(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
4.0ms
(/ (sin x) (sin (* 0.5 x)))
29.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
178.0ms
(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
43.0ms
(/ (sin x) (sin (* 0.5 x)))
105.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify89.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06601767
132211475
250021433

prune595.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin x) (sin (* 0.5 x)))
0.2b
(expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))))
0.2b
(log1p (expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))))
0.2b
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
16×associate-*l*
13×sqrt-prod
11×add-exp-log add-cbrt-cube
9×pow1
5×log1p-expm1-u
4×expm1-log1p-u sqrt-div add-log-exp
3×pow-prod-down associate-*l/ prod-exp associate-/r* cbrt-unprod associate-/l*
2×div-inv
1×cbrt-undiv frac-times log1p-udef expm1-log1p frac-2neg log1p-expm1 associate-*r/ div-exp associate-*r* clear-num *-commutative expm1-udef
Counts
4 → 87
Calls
4 calls:
4.0ms
(/ (sin x) (sin (* 0.5 x)))
0.0ms
(expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))))
0.0ms
(log1p (expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))))
29.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series1.2s

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (sin x) (sin (* 0.5 x)))
163.0ms
(expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))))
855.0ms
(log1p (expm1 (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))))
115.0ms
(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify136.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0383864
11276738
24361729
35001728

prune395.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01915
12115
22115

end0.0ms

sample1.8s

Algorithm
intervals
Results
751.0ms1513×body1280valid
396.0ms1231×body640valid
279.0ms4339×body80valid
143.0ms622×body320valid
50.0ms295×body160valid