Details

Time bar (total: 46.3s)

sample678.0ms

Algorithm
intervals
Results
323.0ms59×body2560valid
140.0ms74×body1280valid
119.0ms64×body640valid
28.0ms33×body320valid
8.0ms15×body160valid
3.0ms11×body80valid

simplify40.0ms

Calls
1 calls:
Slowest
39.0ms
(/ (- x (sin x)) (- x (tan x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize45.0ms

Local error

Found 3 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite41.0ms

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
Calls
3 calls:
Slowest
17.0ms
(/ (- x (sin x)) (- x (tan x)))
16.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series288.0ms

Calls
3 calls:
Slowest
148.0ms
(/ (- x (sin x)) (- x (tan x)))
77.0ms
(- x (sin x))
63.0ms
(- x (tan x))

simplify5.9s

Calls
122 calls:
Slowest
553.0ms
(- (+ 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)))))
435.0ms
(- (+ 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)))))
327.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (- x (tan x)) (- x (tan x))) (- x (tan x))))
300.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
227.0ms
(- (+ (* 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

localize44.0ms

Local error

Found 4 expressions with local error:

27.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
2.2b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.7b
(- x (sin x))
0.5b
(cbrt x)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-cbrt-cube add-exp-log add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-prod associate-/r* fma-neg
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg pow1/3 diff-log div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
14.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
6.0ms
(- x (sin x))
1.0ms
(cbrt x)
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.7s

Calls
4 calls:
Slowest
828.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
515.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
265.0ms
(cbrt x)
59.0ms
(- x (sin x))

simplify4.2s

Calls
80 calls:
Slowest
379.0ms
(/ (* (* (- x (sin x)) (- x (sin x))) (- x (sin x))) (* (* (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))))
307.0ms
(- (* 1/3 (pow x 3)))
250.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))
175.0ms
(fma 1 x (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
170.0ms
(fma (- (cbrt (sin x))) (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x)))))

prune988.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(- x (sin x))
0.6b
(- x (tan x))
0.5b
(expm1 (/ (- x (sin x)) (- x (tan x))))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-cbrt-cube fma-neg add-exp-log
5×associate-/r* log1p-expm1-u associate-/l*
4×expm1-log1p-u pow1 flip3-- insert-posit16 flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv expm1-log1p clear-num frac-2neg div-sub div-exp div-inv expm1-udef
Calls
4 calls:
Slowest
37.0ms
(/ (- x (sin x)) (- x (tan x)))
11.0ms
(- x (sin x))
10.0ms
(- x (tan x))
1.0ms
(expm1 (/ (- x (sin x)) (- x (tan x))))

series383.0ms

Calls
4 calls:
Slowest
130.0ms
(/ (- x (sin x)) (- x (tan x)))
124.0ms
(expm1 (/ (- x (sin x)) (- x (tan x))))
90.0ms
(- x (tan x))
39.0ms
(- x (sin x))

simplify7.7s

Calls
126 calls:
Slowest
574.0ms
(- (+ 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)))))
568.0ms
(fma (sqrt x) (sqrt x) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
538.0ms
(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
522.0ms
(- (+ (* 1/2 (/ (* (pow (sin x) 2) E) (pow x 2))) (+ (/ (* (sin x) E) (* (cos x) x)) (+ E (* 3/2 (/ (* (pow (sin x) 2) E) (* (pow (cos x) 2) (pow x 2))))))) (+ (* 2 (/ (* (pow (sin x) 2) E) (* (cos x) (pow x 2)))) (+ (/ (* (sin x) E) x) 1)))
454.0ms
(- (+ 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)))))

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

23.3b
(log1p (fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1))
0.2b
(* 351/22400 x)
0.1b
(fma x (* 351/22400 x) 9/40)
0.1b
(fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×fma-udef
1×log1p-udef pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
11.0ms
(* 351/22400 x)
1.0ms
(log1p (fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1))
0.0ms
(fma x (* 351/22400 x) 9/40)
0.0ms
(fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1)

series666.0ms

Calls
4 calls:
Slowest
401.0ms
(log1p (fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1))
138.0ms
(fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1)
98.0ms
(fma x (* 351/22400 x) 9/40)
28.0ms
(* 351/22400 x)

simplify2.7s

Calls
22 calls:
Slowest
475.0ms
(fma (exp -1/2) (fma (* x x) (fma x (* 351/22400 x) 9/40) 1) -1)
401.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
387.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
387.0ms
(- (+ (* 9/40 (* (pow x 2) (exp -1/2))) (+ (exp -1/2) (* 351/22400 (* (pow x 4) (exp -1/2))))) 1)
274.0ms
(- (+ (log (* 351/22400 (exp -1/2))) (* 560/39 (/ 1 (pow x 2)))) (+ (* 4 (log (/ -1 x))) (* 179200/4563 (/ 1 (pow x 4)))))

prune714.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes99.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.3b

bsearch199.0ms

end0.0ms

sample17.3s

Algorithm
intervals
Results
7.7s1706×body2560valid
6.0s2597×body1280valid
2.3s1982×body640valid
770.0ms943×body320valid
279.0ms435×body160valid
133.0ms337×body80valid