Details

Time bar (total: 44.9s)

sample412.0ms

Algorithm
intervals
Results
124.0ms98×body1280valid
112.0ms38×body2560valid
74.0ms60×body640valid
19.0ms38×body320valid
3.0ms8×body160valid
3.0ms14×body80valid

simplify24.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
24.0ms
(/ (- x (sin x)) (- x (tan x)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize20.0ms

Local error

Found 3 expressions with local error:

1.1b
(- x (tan x))
1.1b
(- x (sin x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 113
Calls
3 calls:
Slowest
19.0ms
(/ (- x (sin x)) (- x (tan x)))
7.0ms
(- x (sin x))
7.0ms
(- x (tan x))

series213.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
95.0ms
(/ (- x (sin x)) (- x (tan x)))
76.0ms
(- x (tan x))
42.0ms
(- x (sin x))

simplify6.5s

Counts
122 → 122
Calls
122 calls:
Slowest
498.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
497.0ms
(- (+ 1 (+ (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow x 2))) (/ (sin x) (* (cos x) x)))) (+ (/ (sin x) x) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))
429.0ms
(fma (- (sqrt (tan x))) (sqrt (tan x)) (* (sqrt (tan x)) (sqrt (tan x))))
327.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
288.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

27.0b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
1.3b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.1b
(- x (sin x))
0.6b
(cbrt x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-cbrt-cube add-exp-log add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-prod associate-/r* fma-neg
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg pow1/3 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 95
Calls
4 calls:
Slowest
30.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
6.0ms
(- x (sin x))
1.0ms
(cbrt x)
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
790.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
513.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
296.0ms
(cbrt x)
58.0ms
(- x (sin x))

simplify4.1s

Counts
80 → 107
Calls
80 calls:
Slowest
380.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))))
239.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
212.0ms
(- (* 1/3 (pow x 3)))
152.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))
150.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

27.0b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
27.0b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
1.3b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.3b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
30×times-frac
24×add-cube-cbrt
10×associate-/l*
8×add-cbrt-cube add-exp-log distribute-lft-out-- difference-of-squares
6×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp fma-udef div-inv flip--
Counts
4 → 104
Calls
4 calls:
Slowest
38.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
31.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
748.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
722.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
442.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
429.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify5.0s

Counts
94 → 116
Calls
94 calls:
Slowest
491.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))))
364.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))))
278.0ms
(- (* 1/3 (pow x 3)))
267.0ms
(- (* 1/3 (pow x 3)))
96.0ms
(- (pow x 3) (pow (sin x) 3))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

17.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.1b
(* (* x x) (* x x))
0.1b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
114×pow1
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
15×add-cbrt-cube add-exp-log
13×pow2
8×prod-exp cbrt-unprod
3×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
3 → 88
Calls
3 calls:
Slowest
35.0ms
(* (* x x) (* x x))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

series234.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
61.0ms
(* (* x x) (* x x))
61.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify2.9s

Counts
76 → 97
Calls
76 calls:
Slowest
420.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
410.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
338.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
311.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
198.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune806.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes135.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch206.0ms

end0.0ms

sample16.3s

Algorithm
intervals
Results
7.6s1644×body2560valid
5.0s2753×body1280valid
2.5s1788×body640valid
758.0ms1006×body320valid
200.0ms464×body160valid
86.0ms345×body80valid