Details

Time bar (total: 29.8s)

sample758.0ms

Algorithm
intervals
Results
311.0ms51×body2560valid
199.0ms91×body1280valid
107.0ms64×body640valid
24.0ms31×body320valid
7.0ms12×body160valid
2.0ms7×body80valid

simplify26.0ms

Calls
1 calls:
Slowest
26.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize17.0ms

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)))

rewrite8.0ms

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×pow1 associate-/r* insert-posit16 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
4.0ms
(/ (- x (sin x)) (- x (tan x)))
2.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series499.0ms

Calls
3 calls:
Slowest
356.0ms
(- x (sin x))
90.0ms
(/ (- x (sin x)) (- x (tan x)))
52.0ms
(- x (tan x))

simplify2.0s

Calls
39 calls:
Slowest
346.0ms
(- (+ 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)))))
318.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
312.0ms
(- (+ 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)))))
180.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
119.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune597.0ms

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)))

rewrite10.0ms

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×pow1 associate-/r* insert-posit16 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))

series219.0ms

Calls
3 calls:
Slowest
121.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
38.0ms
(- x (sin x))

simplify2.0s

Calls
39 calls:
Slowest
317.0ms
(- (+ 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)))))
314.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
311.0ms
(- (+ 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)))))
228.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
125.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune561.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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))))

rewrite14.0ms

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×insert-posit16 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)))
3.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.0ms
(- x (sin x))
1.0ms
(- x (tan x))

series316.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (- x (tan x)) (- x (sin x)))
96.0ms
(/ 1 (/ (- x (tan x)) (- x (sin x))))
64.0ms
(- x (tan x))
51.0ms
(- x (sin x))

simplify3.0s

Calls
59 calls:
Slowest
324.0ms
(- (+ (/ (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)))))
291.0ms
(- (+ 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)))))
288.0ms
(- (+ (/ (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)))))
273.0ms
(/ (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))) (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))))
246.0ms
(- (+ 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)))))

prune822.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

18.8b
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
0.1b
(* (* x x) 9/40)
0.1b
(* (pow x 4) 27/2800)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
3×pow1 add-cbrt-cube add-exp-log insert-posit16
2×sub-neg *-commutative associate--r+
1×flip3-- diff-log flip-- associate--r-
Calls
3 calls:
Slowest
14.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
5.0ms
(* (* x x) 9/40)
5.0ms
(* (pow x 4) 27/2800)

series58.0ms

Calls
3 calls:
Slowest
25.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
18.0ms
(* (* x x) 9/40)
15.0ms
(* (pow x 4) 27/2800)

simplify527.0ms

Calls
14 calls:
Slowest
140.0ms
(/ (exp (* (* x x) 9/40)) (exp (- (* (pow x 4) 27/2800) -1/2)))
122.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
91.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
89.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
16.0ms
(* 9/40 (pow x 2))

prune381.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

100% (0.0b remaining)

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

bsearch175.0ms

end0.0ms

sample17.6s

Algorithm
intervals
Results
8.0s1670×body2560valid
5.9s2741×body1280valid
2.3s1848×body640valid
811.0ms910×body320valid
231.0ms471×body160valid
130.0ms360×body80valid