Details

Time bar (total: 1.4m)

sample156.0ms

Algorithm
intervals
Results
77.0ms54×body2560valid
25.0ms56×body640valid
24.0ms36×body1280valid
11.0ms31×body320valid
7.0ms67×body80valid
3.0ms12×body160valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
31.0ms
(/ (- 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:

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

rewrite31.0ms

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
25.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series90.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(/ (- 1 (cos x)) (* x x))
25.0ms
(- 1 (cos x))

simplify5.1s

Counts
65 → 53
Calls
65 calls:
Slowest
782.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
757.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
718.0ms
(* (* (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x))) (/ (- 1 (cos x)) (* x x)))
378.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
360.0ms
(* (* x x) (+ (* 1 1) (+ (* (cos x) (cos x)) (* 1 (cos x)))))

prune404.0ms

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)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
24×*-un-lft-identity
22×times-frac
16×add-sqr-sqrt
14×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×flip3-+ flip-+ insert-posit16 div-inv
3×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 → 115
Calls
4 calls:
Slowest
29.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
26.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
21.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series183.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
67.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
66.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
32.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify17.4s

Counts
148 → 127
Calls
148 calls:
Slowest
706.0ms
(/ (/ (* (* (* (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)))
703.0ms
(/ (/ (* (* (* (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)))
682.0ms
(/ (/ (* (* (* (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)))
658.0ms
(/ (/ (* (sin x) (sin x)) (- (* 1 1) (* (cos x) (cos x)))) x)
653.0ms
(/ (/ (* (* (* (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)))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize35.0ms

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×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
20.0ms
(/ (sin x) x)
18.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
7.0ms
(/ (tan (/ x 2)) x)

series235.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
125.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
75.0ms
(/ (tan (/ x 2)) x)
35.0ms
(/ (sin x) x)

simplify9.8s

Counts
141 → 117
Calls
141 calls:
Slowest
667.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)))
514.0ms
(* (* (* (/ (sin x) x) (/ (tan (/ x 2)) x)) (* (/ (sin x) x) (/ (tan (/ x 2)) x))) (* (/ (sin x) x) (/ (tan (/ x 2)) x)))
456.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
404.0ms
(/ (sin (* 1/2 x)) (* (cos (* 1/2 x)) x))
370.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))

prune998.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (sin x))
0.2b
(/ 1 (/ x (sin x)))
0.1b
(/ (tan (/ x 2)) x)
0.1b
(* (/ 1 (/ x (sin x))) (/ (tan (/ x 2)) x))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
137×add-sqr-sqrt
108×*-un-lft-identity
104×add-cube-cbrt
64×add-exp-log
44×associate-*l*
34×add-cbrt-cube
30×div-exp
19×associate-/r*
14×cbrt-undiv prod-exp
13×associate-*r*
12×div-inv
10×unswap-sqr
9×associate-/l*
7×pow1
6×rec-exp 1-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×associate-/r/
1×frac-times pow-prod-down associate-*l/ tan-quot associate-*r/ *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 234
Calls
4 calls:
Slowest
42.0ms
(* (/ 1 (/ x (sin x))) (/ (tan (/ x 2)) x))
20.0ms
(/ 1 (/ x (sin x)))
12.0ms
(/ (tan (/ x 2)) x)
9.0ms
(/ x (sin x))

series252.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(* (/ 1 (/ x (sin x))) (/ (tan (/ x 2)) x))
65.0ms
(/ (tan (/ x 2)) x)
40.0ms
(/ 1 (/ x (sin x)))
40.0ms
(/ x (sin x))

simplify39.4s

Counts
315 → 246
Calls
315 calls:
Slowest
653.0ms
(+ (- (log 1) (- (log x) (log (sin x)))) (- (log (tan (/ x 2))) (log x)))
650.0ms
(+ (- 0 (- (log x) (log (sin x)))) (- (log (tan (/ x 2))) (log x)))
645.0ms
(* (/ 1 (/ x (sin x))) (/ (* (cbrt (tan (/ x 2))) (cbrt (tan (/ x 2)))) 1))
628.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
555.0ms
(+ (- 0 (- (log x) (log (sin x)))) (log (/ (tan (/ x 2)) x)))

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.3s1667×body2560valid
945.0ms1218×body1280valid
741.0ms1466×body640valid
346.0ms2210×body80valid
312.0ms965×body320valid
101.0ms474×body160valid