Details

Time bar (total: 42.6s)

sample512.0ms

Algorithm
intervals
Results
182.0ms52×body2560valid
105.0ms81×body1280valid
89.0ms60×body640valid
22.0ms37×body320valid
6.0ms17×body160valid
2.0ms9×body80valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(/ (- x (sin x)) (- x (tan x)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize24.0ms

Local error

Found 3 expressions with local error:

1.6b
(- x (sin x))
1.5b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×associate-/r* add-cbrt-cube add-exp-log associate-/l*
4×flip3-- flip--
3×pow1 insert-posit16
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
3 → 83
Calls
3 calls:
Slowest
30.0ms
(/ (- x (sin x)) (- x (tan x)))
12.0ms
(- x (sin x))
9.0ms
(- x (tan x))

series245.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
112.0ms
(/ (- x (sin x)) (- x (tan x)))
77.0ms
(- x (tan x))
56.0ms
(- x (sin x))

simplify3.1s

Counts
82 → 92
Calls
82 calls:
Slowest
422.0ms
(- (+ 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)))))
381.0ms
(- (+ 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)))))
359.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
302.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
160.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune794.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

15.6b
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
0.3b
(* (* (* x x) (* x x)) 27/2800)
0.1b
(* (* x x) 9/40)
0.1b
(* (* x x) (* x x))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
138×pow1
39×add-cbrt-cube pow-prod-down add-exp-log
36×pow-prod-up
24×prod-exp cbrt-unprod
22×pow-sqr
18×pow-plus
13×pow2
9×add-log-exp
8×add-sqr-sqrt
7×associate-*r*
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16
3×associate-*l* *-commutative unswap-sqr
2×diff-log
1×sum-log sub-neg flip3-- swap-sqr flip-- associate--r+
Counts
4 → 128
Calls
4 calls:
Slowest
141.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
94.0ms
(* (* (* x x) (* x x)) 27/2800)
40.0ms
(* (* x x) (* x x))
22.0ms
(* (* x x) 9/40)

series218.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(- (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))
53.0ms
(* (* (* x x) (* x x)) 27/2800)
51.0ms
(* (* x x) (* x x))
43.0ms
(* (* x x) 9/40)

simplify6.9s

Counts
111 → 140
Calls
111 calls:
Slowest
635.0ms
(* (* (* x x) (* x x)) 27/2800)
498.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
441.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 27/2800 27/2800) 27/2800))
405.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 27/2800 27/2800) 27/2800))
393.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))

prune948.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.5b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b
(/ (sin x) (- x (tan x)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
44×add-sqr-sqrt
33×times-frac
18×distribute-lft-out--
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
6×flip3-- add-cbrt-cube add-exp-log associate-/r/ flip--
5×associate-/r*
4×pow1 insert-posit16
3×sub-neg distribute-rgt-out-- diff-log div-inv associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 98
Calls
4 calls:
Slowest
51.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
19.0ms
(/ (sin x) (- x (tan x)))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series540.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
87.0ms
(- x (tan x))
86.0ms
(/ (sin x) (- x (tan x)))
66.0ms
(- x (tan x))

simplify4.1s

Counts
95 → 110
Calls
95 calls:
Slowest
412.0ms
(- (+ 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)))))
394.0ms
(- (+ 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)))))
271.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
249.0ms
(- (/ x (- (pow x 3) (pow (tan x) 3))) (/ (sin x) (- (pow x 3) (pow (tan x) 3))))
235.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))

prune974.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
1.6b
(- x (sin x))
1.5b
(- (* x x) (* (tan x) (tan x)))
0.3b
(* (tan x) (tan x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
22×add-sqr-sqrt
18×add-cube-cbrt
16×times-frac
11×pow1
8×add-cbrt-cube add-exp-log add-log-exp
7×difference-of-squares
5×distribute-lft-out
4×associate-/r* tan-quot insert-posit16 associate-/l*
3×flip3-- swap-sqr associate-*r* associate-*l* flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×pow2 frac-times cbrt-undiv clear-num frac-2neg flip3-+ pow-plus div-sub div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 100
Calls
4 calls:
Slowest
19.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
13.0ms
(* (tan x) (tan x))
7.0ms
(- (* x x) (* (tan x) (tan x)))
5.0ms
(- x (sin x))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
111.0ms
(- (* x x) (* (tan x) (tan x)))
46.0ms
(- x (sin x))
41.0ms
(* (tan x) (tan x))

simplify5.8s

Counts
90 → 112
Calls
90 calls:
Slowest
280.0ms
(- (pow x 2) (/ (pow (sin x) 2) (pow (cos x) 2)))
269.0ms
(- (pow x 2) (/ (pow (sin x) 2) (pow (cos x) 2)))
254.0ms
(- (* (* x x) (* x x)) (* (* (tan x) (tan x)) (* (tan x) (tan x))))
246.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
233.0ms
(/ (* (* (- (* x x) (* (tan x) (tan x))) (- (* x x) (* (tan x) (tan x)))) (- (* x x) (* (tan x) (tan x)))) (* (* (+ x (tan x)) (+ x (tan x))) (+ x (tan x))))

prune862.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch167.0ms

end0.0ms

sample16.2s

Algorithm
intervals
Results
7.2s1601×body2560valid
5.3s2811×body1280valid
2.0s1855×body640valid
793.0ms908×body320valid
704.0ms489×body160valid
81.0ms336×body80valid