Details

Time bar (total: 54.2s)

sample157.0ms

Algorithm
intervals
Results
52.0ms54×body2560valid
49.0ms56×body640valid
26.0ms36×body1280valid
10.0ms31×body320valid
7.0ms67×body80valid
3.0ms12×body160valid

simplify44.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
43.0ms
(/ (- 1 (cos x)) (* x x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize11.0ms

Local error

Found 2 expressions with local error:

16.8b
(/ (- 1 (cos x)) (* x x))
1.6b
(- 1 (cos x))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
6×times-frac associate-/l* difference-of-squares
4×add-log-exp
3×fma-neg distribute-lft-out--
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp insert-posit16 log1p-expm1-u flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 63
Calls
2 calls:
Slowest
25.0ms
(- 1 (cos x))
20.0ms
(/ (- 1 (cos x)) (* x x))

series102.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(/ (- 1 (cos x)) (* x x))
26.0ms
(- 1 (cos x))

simplify6.7s

Counts
90 → 69
Calls
90 calls:
Slowest
756.0ms
(* (* (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x))) (/ (- 1 (cos x)) (* x x)))
752.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
623.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
426.0ms
(* (* x x) (+ (* 1 1) (+ (* (cos x) (cos x)) (* 1 (cos x)))))
423.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))

prune570.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

16.5b
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.5b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.2b
(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
25×*-un-lft-identity
22×times-frac
17×add-sqr-sqrt
15×add-cube-cbrt
12×cbrt-undiv div-exp
11×pow1 associate-/l*
7×prod-exp cbrt-unprod
6×associate-/r/ add-log-exp
5×associate-/r* distribute-lft-out
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u div-inv
3×fma-def div-sub swap-sqr associate-*r* associate-*l* sqr-sin
2×clear-num frac-2neg sin-mult associate-/l/
1×pow2 +-commutative sum-log pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 126
Calls
4 calls:
Slowest
29.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
28.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
13.0ms
(* (sin x) (sin x))
6.0ms
(+ 1 (cos x))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
60.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms
(* (sin x) (sin x))
15.0ms
(+ 1 (cos x))

simplify19.0s

Counts
156 → 138
Calls
156 calls:
Slowest
741.0ms
(/ (/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) x) (* (* x x) x)))
741.0ms
(/ (/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) (* x x)) (* x x)))
665.0ms
(/ (/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* x x) x) (* (* x x) x)))
627.0ms
(/ (pow (sin x) 2) (* (pow x 2) (+ (cos x) 1)))
604.0ms
(/ (* x x) (/ (sin x) (+ 1 (cos x))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 114
Calls
3 calls:
Slowest
28.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
10.0ms
(/ (sin x) x)
7.0ms
(/ (tan (/ x 2)) x)

series219.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
108.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
74.0ms
(/ (tan (/ x 2)) x)
37.0ms
(/ (sin x) x)

simplify10.1s

Counts
147 → 123
Calls
147 calls:
Slowest
670.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)))
492.0ms
(* (* (* (/ (sin x) x) (/ (tan (/ x 2)) x)) (* (/ (sin x) x) (/ (tan (/ x 2)) x))) (* (/ (sin x) x) (/ (tan (/ x 2)) x)))
473.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))
442.0ms
(* (/ (sin x) x) (/ (* (cbrt (tan (/ x 2))) (cbrt (tan (/ x 2)))) (* (cbrt x) (cbrt x))))
407.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))

prune972.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×times-frac
21×*-un-lft-identity add-cube-cbrt
19×add-cbrt-cube add-exp-log
13×associate-*l*
6×cbrt-undiv associate-/r* div-exp
5×pow1
4×prod-exp tan-quot cbrt-unprod associate-/l*
3×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
2×frac-times clear-num frac-2neg associate-*l/ associate-*r/ unswap-sqr
1×pow-prod-down *-commutative
Counts
3 → 96
Calls
3 calls:
Slowest
40.0ms
(* (/ (sin x) x) (tan (/ x 2)))
19.0ms
(/ (* (/ (sin x) x) (tan (/ x 2))) x)
15.0ms
(/ (sin x) x)

series304.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(/ (* (/ (sin x) x) (tan (/ x 2))) x)
111.0ms
(* (/ (sin x) x) (tan (/ x 2)))
58.0ms
(/ (sin x) x)

simplify8.1s

Counts
121 → 105
Calls
121 calls:
Slowest
848.0ms
(* (* (/ (* (/ (sin x) x) (tan (/ x 2))) x) (/ (* (/ (sin x) x) (tan (/ x 2))) x)) (/ (* (/ (sin x) x) (tan (/ x 2))) x))
431.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
393.0ms
(/ (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2)))) (* (* x x) x))
361.0ms
(/ (* (* (* (/ (sin x) x) (tan (/ x 2))) (* (/ (sin x) x) (tan (/ x 2)))) (* (/ (sin x) x) (tan (/ x 2)))) (* (* x x) x))
323.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))))

prune982.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.9s1667×body2560valid
1.3s1466×body640valid
809.0ms1218×body1280valid
706.0ms965×body320valid
231.0ms2210×body80valid
111.0ms474×body160valid