Details

Time bar (total: 4.3m)

sample589.0ms

Algorithm
intervals
Results
223.0ms52×body2560valid
174.0ms81×body1280valid
56.0ms60×body640valid
26.0ms37×body320valid
9.0ms17×body160valid
3.0ms9×body80valid

simplify46.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
46.0ms
(/ (- x (sin x)) (- x (tan x)))

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize36.0ms

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)))

rewrite68.0ms

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
36.0ms
(/ (- x (sin x)) (- x (tan x)))
15.0ms
(- x (sin x))
11.0ms
(- x (tan x))

series255.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
106.0ms
(/ (- x (sin x)) (- x (tan x)))
82.0ms
(- x (tan x))
67.0ms
(- x (sin x))

simplify6.0s

Counts
122 → 122
Calls
122 calls:
Slowest
552.0ms
(- (+ 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)))))
538.0ms
(- (+ 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)))))
331.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
320.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
198.0ms
(fma 1 x (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

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
52.0ms
(* (* x x) (* x x))
1.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
0.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)

series256.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
134.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
62.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
61.0ms
(* (* x x) (* x x))

simplify2.6s

Counts
76 → 97
Calls
76 calls:
Slowest
366.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
341.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
283.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
280.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
131.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune709.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)))

rewrite125.0ms

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
75.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
12.0ms
(/ (sin x) (- x (tan x)))
10.0ms
(- x (tan x))
10.0ms
(- x (tan x))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
305.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
106.0ms
(/ (sin x) (- x (tan x)))
92.0ms
(- x (tan x))
87.0ms
(- x (tan x))

simplify3.6m

Counts
1036 → 604
Calls
1036 calls:
Slowest
870.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))
674.0ms
(fma (/ 1 (sqrt (- x (tan x)))) (/ x (sqrt (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
616.0ms
(fma (/ 1 1) (/ x (- x (tan x))) (- (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))))))
599.0ms
(fma (- (/ (sqrt (sin x)) (- x (tan x)))) (/ (sqrt (sin x)) 1) (* (/ (sqrt (sin x)) (- x (tan x))) (/ (sqrt (sin x)) 1)))
596.0ms
(fma (- (/ (sin x) (cbrt (- x (tan x))))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (* (/ (sin x) (cbrt (- x (tan x)))) (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x)))))))

prune5.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

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))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
25×add-cube-cbrt
16×times-frac
11×pow1
10×prod-diff
8×add-cbrt-cube add-exp-log add-log-exp
7×difference-of-squares
5×distribute-lft-out
4×expm1-log1p-u associate-/r* fma-neg tan-quot insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
Slowest
31.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
29.0ms
(* (tan x) (tan x))
8.0ms
(- (* x x) (* (tan x) (tan x)))
6.0ms
(- x (sin x))

series459.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))
124.0ms
(- (* x x) (* (tan x) (tan x)))
60.0ms
(- x (sin x))
41.0ms
(* (tan x) (tan x))

simplify8.9s

Counts
112 → 134
Calls
112 calls:
Slowest
389.0ms
(- (pow x 2) (/ (pow (sin x) 2) (pow (cos x) 2)))
324.0ms
(- (* (* x x) (* x x)) (* (* (tan x) (tan x)) (* (tan x) (tan x))))
319.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
311.0ms
(- (pow x 2) (/ (pow (sin x) 2) (pow (cos x) 2)))
266.0ms
(/ (* (* (- (* 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))))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes356.0ms

Accuracy

100% (0.0b remaining)

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

bsearch146.0ms

end0.0ms

sample17.2s

Algorithm
intervals
Results
7.0s1601×body2560valid
6.5s2811×body1280valid
2.4s1855×body640valid
682.0ms908×body320valid
277.0ms489×body160valid
126.0ms336×body80valid