Details

Time bar (total: 18.1s)

sample189.0ms

Algorithm
intervals
Results
61.0ms48×body2560valid
61.0ms50×body1280valid
28.0ms45×body640valid
12.0ms28×body320valid
9.0ms70×body80valid
4.0ms15×body160valid

simplify62.0ms

Calls
1 calls:
Slowest
62.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize22.0ms

Local error

Found 2 expressions with local error:

15.4b
(/ (- 1 (cos x)) (* x x))
2.5b
(- 1 (cos x))

rewrite29.0ms

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×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u 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
25.0ms
(/ (- 1 (cos x)) (* x x))
2.0ms
(- 1 (cos x))

series78.0ms

Calls
2 calls:
Slowest
52.0ms
(/ (- 1 (cos x)) (* x x))
26.0ms
(- 1 (cos x))

simplify1.2s

Calls
19 calls:
Slowest
641.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
136.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
103.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
68.0ms
(- (log (- 1 (cos x))) (log (* x x)))
52.0ms
(/ (- 1 (cos x)) (pow x 2))

prune367.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

15.3b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite30.0ms

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×expm1-log1p-u cbrt-undiv div-exp associate-*l* associate-*r/ insert-posit16 log1p-expm1-u 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
11.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
9.0ms
(* (sin x) (sin x))
8.0ms
(* (* x x) (+ 1 (cos x)))
1.0ms
(+ 1 (cos x))

series114.0ms

Calls
4 calls:
Slowest
47.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
35.0ms
(* (* x x) (+ 1 (cos x)))
24.0ms
(* (sin x) (sin x))
9.0ms
(+ 1 (cos x))

simplify7.5s

Calls
51 calls:
Slowest
1.3s
(/ (* (* (* (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)))))
879.0ms
(/ (* (* (* (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)))))
849.0ms
(/ (* (* (* (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)))))
831.0ms
(/ (* (* (* (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)))))
438.0ms
(- (log (* (sin x) (sin x))) (+ (log (* x x)) (log (+ 1 (cos x)))))

prune848.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u div-inv add-log-exp
3×fma-def
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
7.0ms
(* (/ (sin x) x) (/ (sin x) x))
3.0ms
(+ (cos x) 1)
3.0ms
(/ (sin x) x)
3.0ms
(/ (sin x) x)

series96.0ms

Calls
4 calls:
Slowest
30.0ms
(/ (sin x) x)
29.0ms
(/ (sin x) x)
27.0ms
(* (/ (sin x) x) (/ (sin x) x))
9.0ms
(+ (cos x) 1)

simplify951.0ms

Calls
34 calls:
Slowest
186.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
134.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
133.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
132.0ms
(- (+ (* 2/45 (pow x 4)) 1) (* 1/3 (pow x 2)))
112.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))

prune804.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/r*
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u div-inv add-log-exp
3×clear-num fma-def frac-2neg associate-/l*
1×+-commutative rec-exp flip3-+ associate-/r/ flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
7.0ms
(+ (cos x) 1)
6.0ms
(/ (sin x) x)
2.0ms
(/ 1 (/ x (sin x)))
1.0ms
(/ x (sin x))

series102.0ms

Calls
4 calls:
Slowest
36.0ms
(/ 1 (/ x (sin x)))
31.0ms
(/ x (sin x))
22.0ms
(/ (sin x) x)
14.0ms
(+ (cos x) 1)

simplify526.0ms

Calls
25 calls:
Slowest
144.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))
128.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
105.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
49.0ms
(+ (* 1/6 (pow x 2)) (+ (* 7/360 (pow x 4)) 1))
12.0ms
(/ 1 (sin x))

prune758.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s1595×body2560valid
847.0ms1245×body1280valid
725.0ms1430×body640valid
541.0ms425×body160valid
289.0ms1001×body320valid
273.0ms2304×body80valid