Details

Time bar (total: 36.9s)

sample148.0ms

Algorithm
intervals
Results
48.0ms43×body2560valid
36.0ms51×body1280valid
32.0ms54×body640valid
9.0ms71×body80valid
8.0ms21×body320valid
3.0ms16×body160valid

simplify68.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize42.0ms

Local error

Found 2 expressions with local error:

14.7b
(/ (- 1 (cos x)) (* x x))
1.5b
(- 1 (cos x))

rewrite42.0ms

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
33.0ms
(/ (- 1 (cos x)) (* x x))
8.0ms
(- 1 (cos x))

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (- 1 (cos x)) (* x x))
20.0ms
(- 1 (cos x))

simplify4.0s

Counts
55 → 69
Calls
55 calls:
Slowest
767.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
690.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
376.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
165.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
157.0ms
(fma (sqrt 1) (sqrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune585.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

14.9b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.3b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
16×pow1
14×*-un-lft-identity
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt
7×associate-*r*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×fma-def flip3-+ swap-sqr flip-+
2×associate-/r/ *-commutative sqr-sin sin-mult distribute-lft-out unswap-sqr
1×pow2 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in times-frac pow-plus div-sub pow-sqr pow-prod-up div-inv associate-/l* associate-/l/
Counts
4 → 107
Calls
4 calls:
Slowest
55.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
43.0ms
(* (* x x) (+ 1 (cos x)))
22.0ms
(* (sin x) (sin x))
10.0ms
(+ 1 (cos x))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
65.0ms
(* (* x x) (+ 1 (cos x)))
25.0ms
(* (sin x) (sin x))
11.0ms
(+ 1 (cos x))

simplify12.5s

Counts
75 → 119
Calls
75 calls:
Slowest
1.2s
(/ (* (* (* (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)))))
1.2s
(/ (* (* (* (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)))))
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)))))
991.0ms
(/ (* (* (* (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)))))
965.0ms
(/ (* (* (* (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)))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
58×times-frac
51×*-un-lft-identity
49×add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
6×cbrt-undiv associate-/r* div-exp div-inv associate-/l* add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def
2×clear-num frac-2neg
1×pow2 frac-times +-commutative sum-log flip3-+ pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ distribute-lft-out
Counts
4 → 148
Calls
4 calls:
Slowest
30.0ms
(* (/ (sin x) x) (/ (sin x) x))
19.0ms
(/ (sin x) x)
15.0ms
(/ (sin x) x)
9.0ms
(+ (cos x) 1)

series195.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(* (/ (sin x) x) (/ (sin x) x))
58.0ms
(/ (sin x) x)
40.0ms
(/ (sin x) x)
19.0ms
(+ (cos x) 1)

simplify5.3s

Counts
140 → 160
Calls
140 calls:
Slowest
529.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
446.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
419.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
196.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
184.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(log (exp (+ (cos x) 1)))
0.3b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(exp (+ (cos x) 1))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
42×*-un-lft-identity
40×times-frac
36×add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
9×add-log-exp
8×exp-prod
5×log-pow
4×expm1-log1p-u cbrt-undiv log-prod div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv unswap-sqr
3×fma-def distribute-lft-out
2×sum-log exp-sum rem-exp-log
1×pow2 frac-times +-commutative flip3-+ pow-plus rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 125
Calls
4 calls:
Slowest
22.0ms
(log (exp (+ (cos x) 1)))
19.0ms
(* (/ (sin x) x) (/ (sin x) x))
11.0ms
(exp (+ (cos x) 1))
5.0ms
(+ (cos x) 1)

series138.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(* (/ (sin x) x) (/ (sin x) x))
56.0ms
(exp (+ (cos x) 1))
14.0ms
(log (exp (+ (cos x) 1)))
11.0ms
(+ (cos x) 1)

simplify4.3s

Counts
108 → 137
Calls
108 calls:
Slowest
411.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
314.0ms
(- (+ (exp 2) (* 1/6 (* (exp 2) (pow x 4)))) (* 1/2 (* (exp 2) (pow x 2))))
215.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
207.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)))
183.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s1636×body2560valid
1.3s1249×body1280valid
737.0ms1509×body640valid
386.0ms2255×body80valid
347.0ms855×body320valid
108.0ms496×body160valid