Details

Time bar (total: 44.0s)

sample136.0ms

Algorithm
intervals
Results
50.0ms55×body2560valid
24.0ms46×body1280valid
22.0ms48×body640valid
21.0ms23×body320valid
6.0ms69×body80valid
3.0ms15×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize16.0ms

Local error

Found 2 expressions with local error:

16.2b
(/ (- 1 (cos x)) (* x x))
1.7b
(- 1 (cos x))

rewrite30.0ms

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
23.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series96.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
70.0ms
(/ (- 1 (cos x)) (* x x))
26.0ms
(- 1 (cos x))

simplify4.9s

Counts
65 → 53
Calls
65 calls:
Slowest
696.0ms
(* (* (/ (- 1 (cos x)) (* x x)) (/ (- 1 (cos x)) (* x x))) (/ (- 1 (cos x)) (* x x)))
695.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
642.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
400.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
367.0ms
(* (* x x) (+ (* 1 1) (+ (* (cos x) (cos x)) (* 1 (cos x)))))

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

16.1b
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.2b
(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite96.0ms

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
37.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
22.0ms
(* (sin x) (sin x))
21.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
14.0ms
(+ 1 (cos x))

series194.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
50.0ms
(/ (* (sin x) (sin x)) (+ 1 (cos x)))
20.0ms
(* (sin x) (sin x))
18.0ms
(+ 1 (cos x))

simplify17.4s

Counts
148 → 127
Calls
148 calls:
Slowest
834.0ms
(/ (/ (* (* (* (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)))
684.0ms
(/ (/ (* (* (* (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)))
676.0ms
(/ (/ (* (* (* (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)))
657.0ms
(- (- (+ (log (sin x)) (log (sin x))) (log (+ 1 (cos x)))) (log (* x x)))
630.0ms
(/ (/ (* (* (* (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)))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
10.0ms
(/ (sin x) x)
7.0ms
(/ (tan (/ x 2)) x)

series266.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
131.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
96.0ms
(/ (tan (/ x 2)) x)
39.0ms
(/ (sin x) x)

simplify9.6s

Counts
141 → 117
Calls
141 calls:
Slowest
692.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)))
574.0ms
(* (* (* (/ (sin x) x) (/ (tan (/ x 2)) x)) (* (/ (sin x) x) (/ (tan (/ x 2)) x))) (* (/ (sin x) x) (/ (tan (/ x 2)) x)))
410.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
406.0ms
(* (/ (sin x) x) (/ (* (cbrt (tan (/ x 2))) (cbrt (tan (/ x 2)))) (* (cbrt x) (cbrt x))))
372.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))

prune967.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
0.5b
(* (cbrt x) (cbrt x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
Slowest
15.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series978.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(* (cbrt x) (cbrt x))
251.0ms
(cbrt x)
245.0ms
(cbrt x)
227.0ms
(cbrt x)

simplify1.3s

Counts
103 → 89
Calls
103 calls:
Slowest
184.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
146.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
124.0ms
(* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))
123.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
91.0ms
(* (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt x)))

prune963.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.2s1615×body2560valid
1.3s1460×body640valid
853.0ms1314×body1280valid
374.0ms907×body320valid
269.0ms2202×body80valid
112.0ms502×body160valid