Details

Time bar (total: 4.4m)

sample612.0ms

Algorithm
intervals
Results
170.0ms46×body2560valid
146.0ms80×body1280valid
81.0ms70×body640valid
75.0ms36×body320valid
6.0ms12×body160valid
3.0ms12×body80valid

simplify66.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
66.0ms
(/ (- x (sin x)) (- x (tan x)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize33.0ms

Local error

Found 3 expressions with local error:

1.4b
(- x (sin x))
1.4b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite50.0ms

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
23.0ms
(/ (- x (sin x)) (- x (tan x)))
15.0ms
(- x (sin x))
9.0ms
(- x (tan x))

series256.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
106.0ms
(/ (- x (sin x)) (- x (tan x)))
87.0ms
(- x (tan x))
64.0ms
(- x (sin x))

simplify6.2s

Counts
122 → 122
Calls
122 calls:
Slowest
534.0ms
(- (+ 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)))))
529.0ms
(- (+ 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)))))
347.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
335.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
223.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
0.2b
(/ (sin x) (- x (tan x)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
678×times-frac
459×prod-diff
417×add-cube-cbrt
147×distribute-lft-out--
141×difference-of-squares
92×associate-/r/
49×flip3-- flip--
46×div-inv
27×fma-neg
10×add-log-exp
6×add-cbrt-cube add-exp-log
5×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×sub-neg distribute-rgt-out-- diff-log associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp frac-sub sub-div
Counts
4 → 592
Calls
4 calls:
Slowest
76.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
13.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series494.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
92.0ms
(- x (tan x))
72.0ms
(/ (sin x) (- x (tan x)))
60.0ms
(- x (tan x))

simplify3.6m

Counts
1036 → 604
Calls
1036 calls:
Slowest
765.0ms
(fma (- (/ (cbrt (sin x)) (cbrt (- x (tan x))))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (cbrt (sin x)) (cbrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
746.0ms
(fma (/ 1 (+ (sqrt x) (sqrt (tan x)))) (/ x (- (sqrt x) (sqrt (tan x)))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
719.0ms
(fma (- (/ (cbrt (sin x)) (cbrt (- x (tan x))))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (cbrt (sin x)) (cbrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
715.0ms
(fma (* (cbrt (/ x (- x (tan x)))) (cbrt (/ x (- x (tan x))))) (cbrt (/ x (- x (tan x)))) (- (* (/ (cbrt (sin x)) (sqrt (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (sqrt (- x (tan x)))))))
634.0ms
(fma (/ (sqrt x) 1) (/ (sqrt x) (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))

prune5.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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))
0.0b
(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
34.0ms
(* (* 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))

series268.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
144.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
79.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
45.0ms
(* (* x x) (* x x))

simplify3.1s

Counts
76 → 97
Calls
76 calls:
Slowest
409.0ms
(+ (* 2 1) (+ 1 1))
381.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
350.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
320.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
214.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))

prune760.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

16.8b
(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))
1.4b
(- x (tan x))
1.4b
(- (* x x) (* (sin x) (sin x)))
0.3b
(* (sin x) (sin x))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity
17×add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
10×prod-diff
8×associate-/r/ add-log-exp
6×flip3-- flip--
4×expm1-log1p-u frac-times times-frac fma-neg insert-posit16 log1p-expm1-u associate-/l* difference-of-squares
3×flip3-+ swap-sqr associate-*r* associate-*l* flip-+
2×cbrt-undiv sub-neg diff-log div-exp associate-*l/ prod-exp associate-*r/ cbrt-unprod sqr-sin associate-/l/
1×pow2 clear-num associate-/r* frac-2neg pow-plus div-sub pow-prod-down pow-sqr *-commutative pow-prod-up div-inv sin-mult distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 115
Calls
4 calls:
Slowest
25.0ms
(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))
22.0ms
(- (* x x) (* (sin x) (sin x)))
13.0ms
(* (sin x) (sin x))
6.0ms
(- x (tan x))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))
119.0ms
(- (* x x) (* (sin x) (sin x)))
79.0ms
(- x (tan x))
33.0ms
(* (sin x) (sin x))

simplify9.8s

Counts
92 → 127
Calls
92 calls:
Slowest
950.0ms
(/ (* (* (- (* x x) (* (sin x) (sin x))) (- (* x x) (* (sin x) (sin x)))) (- (* x x) (* (sin x) (sin x)))) (* (* (* (- x (tan x)) (+ x (sin x))) (* (- x (tan x)) (+ x (sin x)))) (* (- x (tan x)) (+ x (sin x)))))
874.0ms
(/ (* (* (- (* x x) (* (sin x) (sin x))) (- (* x x) (* (sin x) (sin x)))) (- (* x x) (* (sin x) (sin x)))) (* (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))) (* (* (+ x (sin x)) (+ x (sin x))) (+ x (sin x)))))
559.0ms
(- (+ 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)))))
496.0ms
(- (+ 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)))))
373.0ms
(- (+ (* 1/315 (pow x 8)) (* 1/3 (pow x 4))) (* 2/45 (pow x 6)))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

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

bsearch114.0ms

end0.0ms

sample17.6s

Algorithm
intervals
Results
8.1s1654×body2560valid
5.3s2790×body1280valid
2.5s1833×body640valid
816.0ms912×body320valid
606.0ms484×body160valid
83.0ms327×body80valid