Details

Time bar (total: 30.7s)

sample650.0ms

Algorithm
intervals
Results
268.0ms51×body2560valid
241.0ms91×body1280valid
67.0ms64×body640valid
20.0ms31×body320valid
4.0ms12×body160valid
2.0ms7×body80valid

simplify29.0ms

Calls
1 calls:
Slowest
28.0ms
(/ (- x (sin x)) (- x (tan x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.9b
(- x (sin x))
0.9b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite472.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
466.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series205.0ms

Calls
3 calls:
Slowest
109.0ms
(/ (- x (sin x)) (- x (tan x)))
57.0ms
(- x (tan x))
39.0ms
(- x (sin x))

simplify2.4s

Calls
39 calls:
Slowest
449.0ms
(- (+ 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)))))
375.0ms
(- (+ 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)))))
362.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
313.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
141.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune734.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize1.0ms

Local error

Found 3 expressions with local error:

0.9b
(- x (sin x))
0.9b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
4×flip3-- flip--
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×sub-neg associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Calls
3 calls:
Slowest
7.0ms
(/ (- x (sin x)) (- x (tan x)))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series201.0ms

Calls
3 calls:
Slowest
97.0ms
(/ (- x (sin x)) (- x (tan x)))
52.0ms
(- x (tan x))
51.0ms
(- x (sin x))

simplify2.3s

Calls
39 calls:
Slowest
400.0ms
(- (+ 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)))))
362.0ms
(- (+ 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)))))
332.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
265.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
152.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune584.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b
(- x (sin x))
0.9b
(- x (tan x))
0.0b
(/ (- x (tan x)) (- x (sin x)))
0.0b
(/ 1 (/ (- x (tan x)) (- x (sin x))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r* times-frac
9×add-exp-log
6×add-cbrt-cube
5×pow1 flip3-- associate-/r/ flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rec-exp clear-num sub-neg frac-2neg div-exp associate-/l/
1×cbrt-undiv div-sub pow-flip inv-pow
Calls
4 calls:
Slowest
7.0ms
(/ (- x (tan x)) (- x (sin x)))
4.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series295.0ms

Calls
4 calls:
Slowest
104.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
83.0ms
(/ (- x (tan x)) (- x (sin x)))
59.0ms
(- x (tan x))
48.0ms
(- x (sin x))

simplify3.3s

Calls
59 calls:
Slowest
352.0ms
(- (+ 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)))))
345.0ms
(- (+ 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)))))
333.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
302.0ms
(/ (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))) (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))))
296.0ms
(- (+ (/ (pow (sin x) 2) (pow x 2)) (+ (/ (sin x) x) 1)) (+ (/ (sin x) (* (cos x) x)) (/ (pow (sin x) 2) (* (cos x) (pow x 2)))))

prune764.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

18.9b
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.2b
(* 9/40 x)
0.1b
(fma (* 9/40 x) x -1/2)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
0.0ms
(* 9/40 x)
0.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
0.0ms
(fma (* 9/40 x) x -1/2)

series71.0ms

Calls
3 calls:
Slowest
41.0ms
(fma (* 9/40 x) x -1/2)
20.0ms
(fma (pow x 4) -27/2800 (fma (* 9/40 x) x -1/2))
10.0ms
(* 9/40 x)

simplify478.0ms

Calls
9 calls:
Slowest
147.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
107.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
106.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
38.0ms
(- (* 9/40 (pow x 2)) 1/2)
36.0ms
(- (* 9/40 (pow x 2)) 1/2)

prune433.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch146.0ms

end0.0ms

sample17.4s

Algorithm
intervals
Results
8.1s1670×body2560valid
4.8s2741×body1280valid
2.7s1848×body640valid
1.2s910×body320valid
286.0ms471×body160valid
126.0ms360×body80valid