Details

Time bar (total: 19.3s)

sample136.0ms

Algorithm
intervals
Results
61.0ms59×body2560valid
23.0ms47×body640valid
19.0ms26×body1280valid
12.0ms35×body320valid
9.0ms75×body80valid
3.0ms14×body160valid

simplify74.0ms

Calls
1 calls:
Slowest
74.0ms
(/ (- 1 (cos x)) (* x x))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize11.0ms

Local error

Found 2 expressions with local error:

16.4b
(/ (- 1 (cos x)) (* x x))
1.0b
(- 1 (cos x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×times-frac associate-/l*
2×pow1 flip3-- insert-posit16 flip-- add-log-exp associate-/l/
1×cbrt-undiv clear-num associate-/r* sub-neg frac-2neg div-sub div-exp div-inv
Calls
2 calls:
Slowest
4.0ms
(/ (- 1 (cos x)) (* x x))
1.0ms
(- 1 (cos x))

series82.0ms

Calls
2 calls:
Slowest
55.0ms
(/ (- 1 (cos x)) (* x x))
26.0ms
(- 1 (cos x))

simplify1.0s

Calls
19 calls:
Slowest
528.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
103.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
78.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
55.0ms
(/ (- 1 (cos x)) (pow x 2))
41.0ms
(- (log (- 1 (cos x))) (log (* x x)))

prune344.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

16.4b
(/ (* (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)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
11×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-*r* prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 add-log-exp
3×flip3-+ flip-+
2×pow-prod-down associate-/r/ *-commutative sqr-sin sin-mult
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-prod-up div-inv associate-/l* associate-/l/
Calls
4 calls:
Slowest
20.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
11.0ms
(* (sin x) (sin x))
9.0ms
(* (* x x) (+ 1 (cos x)))
2.0ms
(+ 1 (cos x))

series197.0ms

Calls
4 calls:
Slowest
102.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
61.0ms
(* (* x x) (+ 1 (cos x)))
19.0ms
(* (sin x) (sin x))
15.0ms
(+ 1 (cos x))

simplify7.2s

Calls
51 calls:
Slowest
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)))))
907.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x))))
833.0ms
(/ (* (* (* (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)))))
830.0ms
(/ (* (* (* (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)))))
657.0ms
(/ (* (* (* (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)))))

prune829.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log associate-/l*
4×associate-*r* associate-*l* insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg
1×pow2 frac-times +-commutative flip3-+ pow-plus pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip-+
Calls
4 calls:
Slowest
9.0ms
(* (/ (sin x) x) (/ (sin x) x))
5.0ms
(/ (sin x) x)
5.0ms
(/ (sin x) x)
3.0ms
(+ (cos x) 1)

series174.0ms

Calls
4 calls:
Slowest
77.0ms
(* (/ (sin x) x) (/ (sin x) x))
43.0ms
(/ (sin x) x)
37.0ms
(/ (sin x) x)
17.0ms
(+ (cos x) 1)

simplify787.0ms

Calls
32 calls:
Slowest
157.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
126.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))
104.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
97.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
71.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))

prune579.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×times-frac
8×add-cbrt-cube add-exp-log
7×div-inv associate-/l*
6×pow1
4×associate-*l* insert-posit16 add-log-exp
3×associate-/r* associate-*r*
2×clear-num frac-2neg flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative div-exp pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
12.0ms
(/ (/ (* (/ (sin x) x) (sin x)) x) (+ (cos x) 1))
6.0ms
(* (/ (sin x) x) (sin x))
5.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)

series224.0ms

Calls
4 calls:
Slowest
91.0ms
(/ (/ (* (/ (sin x) x) (sin x)) x) (+ (cos x) 1))
73.0ms
(* (/ (sin x) x) (sin x))
47.0ms
(/ (sin x) x)
13.0ms
(+ (cos x) 1)

simplify3.2s

Calls
59 calls:
Slowest
388.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (sin x) (sin x)) (sin x)))
278.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
257.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
221.0ms
(/ (* (* (/ (* (/ (sin x) x) (sin x)) x) (/ (* (/ (sin x) x) (sin x)) x)) (/ (* (/ (sin x) x) (sin x)) x)) (* (* (+ (cos x) 1) (+ (cos x) 1)) (+ (cos x) 1)))
184.0ms
(- (log (/ (* (/ (sin x) x) (sin x)) x)) (log (+ (cos x) 1)))

prune699.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.8s1702×body2560valid
599.0ms1540×body640valid
576.0ms1159×body1280valid
222.0ms942×body320valid
168.0ms2214×body80valid
69.0ms443×body160valid