Details

Time bar (total: 40.7s)

sample143.0ms

Algorithm
intervals
Results
72.0ms48×body2560valid
24.0ms58×body640valid
21.0ms42×body1280valid
7.0ms26×body320valid
6.0ms68×body80valid
2.0ms14×body160valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(/ (- 1 (cos x)) (* x x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 2 expressions with local error:

14.3b
(/ (- 1 (cos x)) (* x x))
1.7b
(- 1 (cos x))

rewrite44.0ms

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
37.0ms
(/ (- 1 (cos x)) (* x x))
5.0ms
(- 1 (cos x))

series103.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (- 1 (cos x)) (* x x))
41.0ms
(- 1 (cos x))

simplify4.2s

Counts
55 → 69
Calls
55 calls:
Slowest
723.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) (* x x)) (* x x)))
651.0ms
(/ (* (* (- 1 (cos x)) (- 1 (cos x))) (- 1 (cos x))) (* (* (* x x) x) (* (* x x) x)))
427.0ms
(- (+ (* 1/2 (pow x 2)) (* 1/720 (pow x 6))) (* 1/24 (pow x 4)))
224.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))
198.0ms
(fma 1 1 (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune627.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
0.4b
(+ 1 (cos x))
0.3b
(* (sin x) (sin x))
0.1b
(* (* x x) (+ 1 (cos x)))

rewrite105.0ms

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
48.0ms
(* (* x x) (+ 1 (cos x)))
25.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
21.0ms
(* (sin x) (sin x))
9.0ms
(+ 1 (cos x))

series167.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(/ (* (sin x) (sin x)) (* (* x x) (+ 1 (cos x))))
60.0ms
(* (* 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
1.3s
(/ (* (* (* (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) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))
953.0ms
(/ (* (* (* (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)))))
935.0ms
(/ (* (* (* (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)))))
934.0ms
(/ (* (* (* (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)))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1)
0.2b
(/ (/ (sin x) x) (+ (cos x) 1))
0.1b
(/ (sin x) x)
0.1b
(/ (sin x) x)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
115×times-frac
100×*-un-lft-identity
70×add-sqr-sqrt add-cube-cbrt
19×associate-/l*
15×distribute-lft-out
13×add-cbrt-cube add-exp-log
10×associate-/r*
8×div-inv
6×add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num fma-def frac-2neg
2×flip3-+ associate-/r/ flip-+
1×+-commutative sum-log associate-/l/
Counts
4 → 167
Calls
4 calls:
Slowest
28.0ms
(/ (/ (sin x) x) (+ (cos x) 1))
20.0ms
(/ (sin x) x)
14.0ms
(/ (sin x) x)
6.0ms
(+ (cos x) 1)

series188.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(/ (/ (sin x) x) (+ (cos x) 1))
55.0ms
(/ (sin x) x)
41.0ms
(/ (sin x) x)
18.0ms
(+ (cos x) 1)

simplify7.7s

Counts
191 → 179
Calls
191 calls:
Slowest
484.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
405.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
370.0ms
(/ (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt x) (cbrt x))) (* (cbrt (+ (cos x) 1)) (cbrt (+ (cos x) 1))))
270.0ms
(- (+ (* 1/120 (pow x 4)) 1) (* 1/6 (pow x 2)))
250.0ms
(- (+ (* 1/24 (pow x 4)) 2) (* 1/2 (pow x 2)))

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

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))

rewrite38.0ms

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
22.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
7.0ms
(/ (sin x) x)
6.0ms
(/ (tan (/ x 2)) x)

series240.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
122.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))
79.0ms
(/ (tan (/ x 2)) x)
39.0ms
(/ (sin x) x)

simplify5.2s

Counts
103 → 123
Calls
103 calls:
Slowest
668.0ms
(* (* (* (/ (sin x) x) (/ (sin x) x)) (/ (sin x) x)) (* (* (/ (tan (/ x 2)) x) (/ (tan (/ x 2)) x)) (/ (tan (/ x 2)) x)))
406.0ms
(/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x))
366.0ms
(/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x))
310.0ms
(/ (* (sin x) (sin (* 1/2 x))) (* (cos (* 1/2 x)) (pow x 2)))
302.0ms
(* (/ (* (* (sin x) (sin x)) (sin x)) (* (* x x) x)) (/ (* (* (tan (/ x 2)) (tan (/ x 2))) (tan (/ x 2))) (* (* x x) x)))

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.2s1609×body2560valid
924.0ms1490×body640valid
904.0ms1249×body1280valid
350.0ms940×body320valid
322.0ms2245×body80valid
132.0ms467×body160valid