Details

Time bar (total: 36.6s)

sample153.0ms

Algorithm
intervals
Results
59.0ms47×body2560valid
28.0ms38×body1280valid
24.0ms44×body640valid
14.0ms84×body80valid
12.0ms30×body320valid
3.0ms13×body160valid

simplify86.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
85.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize23.0ms

Local error

Found 2 expressions with local error:

13.6b
(/ (- 1 (cos x)) (* x x))
1.5b
(- 1 (cos x))

rewrite41.0ms

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
30.0ms
(/ (- 1 (cos x)) (* x x))
9.0ms
(- 1 (cos x))

series123.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
93.0ms
(/ (- 1 (cos x)) (* x x))
29.0ms
(- 1 (cos x))

simplify2.5s

Counts
35 → 53
Calls
35 calls:
Slowest
648.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
611.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
290.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
151.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
81.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune491.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (* x x) (+ 1 (cos x)))
0.3b
(* (sin x) (sin x))

rewrite108.0ms

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
44.0ms
(* (* x x) (+ 1 (cos x)))
40.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
13.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series194.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
55.0ms
(* (* x x) (+ 1 (cos x)))
29.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify11.7s

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) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
938.0ms
(/ (* (* (* (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)))))
924.0ms
(/ (* (* (* (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)))))
916.0ms
(/ (* (* (* (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)))))

prune869.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (* (sin x) (sin x)) (* (+ x (* (cos x) x)) x))
0.4b
(+ x (* (cos x) x))
0.3b
(* (sin x) (sin x))
0.1b
(* (cos x) x)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
13×pow1
11×*-un-lft-identity
10×add-cube-cbrt
6×associate-*r* associate-*l* prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv div-exp insert-posit16
3×swap-sqr
2×flip3-+ pow-prod-down associate-*l/ associate-/r/ *-commutative flip-+ sqr-sin sin-mult unswap-sqr
1×pow2 +-commutative clear-num associate-/r* sum-log frac-2neg times-frac pow-plus distribute-rgt-out div-sub distribute-rgt1-in pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 87
Calls
4 calls:
Slowest
22.0ms
(/ (* (sin x) (sin x)) (* (+ x (* (cos x) x)) x))
22.0ms
(* (sin x) (sin x))
15.0ms
(* (cos x) x)
11.0ms
(+ x (* (cos x) x))

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (* (sin x) (sin x)) (* (+ x (* (cos x) x)) x))
72.0ms
(+ x (* (cos x) x))
35.0ms
(* (cos x) x)
33.0ms
(* (sin x) (sin x))

simplify7.8s

Counts
61 → 99
Calls
61 calls:
Slowest
851.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (+ x (* (cos x) x)) x) (* (+ x (* (cos x) x)) x)) (* (+ x (* (cos x) x)) x)))
837.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (+ x (* (cos x) x)) (+ x (* (cos x) x))) (+ x (* (cos x) x))) (* (* x x) x)))
835.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (+ x (* (cos x) x)) x) (* (+ x (* (cos x) x)) x)) (* (+ x (* (cos x) x)) x)))
746.0ms
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (+ x (* (cos x) x)) (+ x (* (cos x) x))) (+ x (* (cos x) x))) (* (* x x) x)))
469.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))

prune806.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity add-cube-cbrt
19×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
6×cbrt-undiv associate-/r* div-exp associate-/l*
5×pow1
4×prod-exp cbrt-unprod div-inv unswap-sqr
3×insert-posit16 add-log-exp
2×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ tan-quot associate-*r/ *-commutative associate-/l/
Counts
3 → 108
Calls
3 calls:
Slowest
29.0ms
(* (/ (tan (/ x 2)) x) (/ (sin x) x))
17.0ms
(/ (tan (/ x 2)) x)
15.0ms
(/ (sin x) x)

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
134.0ms
(* (/ (tan (/ x 2)) x) (/ (sin x) x))
75.0ms
(/ (tan (/ x 2)) x)
45.0ms
(/ (sin x) x)

simplify4.8s

Counts
103 → 117
Calls
103 calls:
Slowest
625.0ms
(* (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
443.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
366.0ms
(* (/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
363.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))
211.0ms
(+ (- (log (tan (/ x 2))) (log x)) (log (/ (sin x) x)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.1s1566×body2560valid
1.2s1258×body1280valid
833.0ms1522×body640valid
335.0ms971×body320valid
279.0ms2176×body80valid
177.0ms507×body160valid