Details

Time bar (total: 1.3m)

sample136.0ms

Algorithm
intervals
Results
68.0ms48×body2560valid
22.0ms58×body640valid
21.0ms42×body1280valid
7.0ms26×body320valid
6.0ms68×body80valid
3.0ms14×body160valid

simplify39.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
39.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 2 expressions with local error:

14.3b
(/ (- 1 (cos x)) (* x x))
1.7b
(- 1 (cos x))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-cube-cbrt add-log-exp
3×distribute-lft-out--
2×pow1 cbrt-undiv flip3-- div-exp insert-posit16 flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 47
Calls
2 calls:
Slowest
31.0ms
(/ (- 1 (cos x)) (* x x))
18.0ms
(- 1 (cos x))

series112.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(/ (- 1 (cos x)) (* x x))
30.0ms
(- 1 (cos x))

simplify2.8s

Counts
35 → 53
Calls
35 calls:
Slowest
731.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
686.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
357.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
202.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
89.0ms
(- (log (- 1 (cos x))) (+ (log x) (log x)))

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
13×*-un-lft-identity prod-exp cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×associate-*l* pow-prod-down associate-*r/ insert-posit16
3×flip3-+ swap-sqr flip-+
2×associate-/r/ *-commutative sqr-sin sin-mult distribute-lft-out unswap-sqr
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 96
Calls
4 calls:
Slowest
46.0ms
(* (* x x) (+ 1 (cos x)))
24.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
23.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
54.0ms
(* (* x x) (+ 1 (cos x)))
22.0ms
(* (sin x) (sin x))
20.0ms
(+ 1 (cos x))

simplify11.9s

Counts
73 → 108
Calls
73 calls:
Slowest
1.2s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.1s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
1.1s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.0s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
829.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))

prune966.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.2b
(/ (+ (cos x) 1) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
115×times-frac
99×*-un-lft-identity
69×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
15×distribute-lft-out
13×add-cbrt-cube add-exp-log
10×associate-/l*
8×div-inv
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1 insert-posit16
3×clear-num frac-2neg
2×flip3-+ flip-+ associate-/l/
1×+-commutative sum-log associate-/r/
Counts
4 → 156
Calls
4 calls:
Slowest
30.0ms
(/ (+ (cos x) 1) (/ (sin x) x))
14.0ms
(/ (sin x) x)
7.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series156.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(/ (+ (cos x) 1) (/ (sin x) x))
39.0ms
(/ (sin x) x)
38.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify8.1s

Counts
187 → 168
Calls
187 calls:
Slowest
487.0ms
(/ (* (cbrt (+ (cos x) 1)) (cbrt (+ (cos x) 1))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
428.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
406.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
327.0ms
(- 2 (+ (* 1/6 (pow x 2)) (* 1/360 (pow x 4))))
206.0ms
(/ (* (cbrt (+ (cos x) 1)) (cbrt (+ (cos x) 1))) (/ 1 (* (cbrt x) (cbrt x))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ x (tan (/ x 2)))
0.1b
(/ (sin x) x)
0.1b
(/ (/ (sin x) x) (/ x (tan (/ x 2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
461×times-frac
222×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×div-inv
20×associate-/r*
19×add-cbrt-cube add-exp-log associate-/l*
16×associate-/r/
15×tan-quot
10×cbrt-undiv div-exp
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×associate-/l/
Counts
3 → 287
Calls
3 calls:
Slowest
19.0ms
(/ (/ (sin x) x) (/ x (tan (/ x 2))))
7.0ms
(/ (sin x) x)
5.0ms
(/ x (tan (/ x 2)))

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
129.0ms
(/ (/ (sin x) x) (/ x (tan (/ x 2))))
89.0ms
(/ x (tan (/ x 2)))
37.0ms
(/ (sin x) x)

simplify41.2s

Counts
459 → 296
Calls
459 calls:
Slowest
649.0ms
(/ (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* x x) x) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)))))
649.0ms
(/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (sqrt x) 1))
602.0ms
(/ (/ 1 (* (cbrt x) (cbrt x))) (/ 1 (* (cbrt (tan (/ x 2))) (cbrt (tan (/ x 2))))))
528.0ms
(/ (/ (sqrt (sin x)) (* (cbrt x) (cbrt x))) (/ 1 (* (cbrt (tan (/ x 2))) (cbrt (tan (/ x 2))))))
522.0ms
(/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ x (sin (/ x 2))))

prune3.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.8s1609×body2560valid
1.4s1249×body1280valid
869.0ms1490×body640valid
518.0ms467×body160valid
312.0ms940×body320valid
236.0ms2245×body80valid