Details

Time bar (total: 37.4s)

sample106.0ms

Algorithm
intervals
Results
33.0ms38×body2560valid
24.0ms47×body1280valid
18.0ms44×body640valid
12.0ms38×body320valid
9.0ms81×body80valid
2.0ms8×body160valid

simplify64.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
64.0ms
(/ (- 1 (cos x)) (* x x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize25.0ms

Local error

Found 2 expressions with local error:

11.4b
(/ (- 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
34.0ms
(/ (- 1 (cos x)) (* x x))
11.0ms
(- 1 (cos x))

series138.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
103.0ms
(/ (- 1 (cos x)) (* x x))
35.0ms
(- 1 (cos x))

simplify3.8s

Counts
55 → 69
Calls
55 calls:
Slowest
695.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
628.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
316.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
168.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
161.0ms
(fma 1 1 (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

11.3b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.5b
(+ 1 (cos x))
0.2b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite95.0ms

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
43.0ms
(* (* x x) (+ 1 (cos x)))
32.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
12.0ms
(* (sin x) (sin x))
5.0ms
(+ 1 (cos x))

series172.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
54.0ms
(* (* x x) (+ 1 (cos x)))
27.0ms
(* (sin x) (sin x))
13.0ms
(+ 1 (cos x))

simplify11.8s

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)))))
1.0s
(/ (* (* (* (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)))))
1.0s
(/ (* (* (* (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)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos x) 1)
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite57.0ms

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
32.0ms
(* (/ (sin x) x) (/ (sin x) x))
8.0ms
(+ (cos x) 1)
8.0ms
(/ (sin x) x)
8.0ms
(/ (sin x) x)

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(* (/ (sin x) x) (/ (sin x) x))
54.0ms
(/ (sin x) x)
35.0ms
(/ (sin x) x)
11.0ms
(+ (cos x) 1)

simplify5.3s

Counts
140 → 160
Calls
140 calls:
Slowest
425.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
424.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
423.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
248.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))
247.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)))

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (exp (cos x)) E)
0.6b
(log (* (exp (cos x)) E))
0.1b
(* (/ (sin x) x) (/ (sin x) x))
0.1b
(/ (sin x) x)

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
49×times-frac
42×*-un-lft-identity add-cube-cbrt
21×add-exp-log
20×add-cbrt-cube
16×pow1 associate-*r* associate-*l*
13×swap-sqr
8×prod-exp
5×cbrt-undiv div-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* rem-log-exp pow-prod-down associate-/l*
2×e-exp-1 log-pow *-commutative
1×pow2 frac-times log-prod clear-num frac-2neg pow-plus associate-*l/ associate-*r/ pow-sqr pow-prod-up
Counts
4 → 138
Calls
4 calls:
Slowest
35.0ms
(* (exp (cos x)) E)
31.0ms
(* (/ (sin x) x) (/ (sin x) x))
22.0ms
(log (* (exp (cos x)) E))
15.0ms
(/ (sin x) x)

series390.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(log (* (exp (cos x)) E))
77.0ms
(* (/ (sin x) x) (/ (sin x) x))
63.0ms
(* (exp (cos x)) E)
53.0ms
(/ (sin x) x)

simplify5.4s

Counts
126 → 150
Calls
126 calls:
Slowest
499.0ms
(* (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))))
429.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
341.0ms
(/ (sqrt (sin x)) (cbrt x))
320.0ms
(- (+ (pow E 2) (* 1/6 (* (pow x 4) (pow E 2)))) (* 1/2 (* (pow x 2) (pow E 2))))
289.0ms
(* (* (* (exp (cos x)) (exp (cos x))) (exp (cos x))) (* (* E E) E))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.3s1636×body2560valid
887.0ms1207×body1280valid
730.0ms1406×body640valid
500.0ms1007×body320valid
286.0ms2277×body80valid
149.0ms467×body160valid