Details

Time bar (total: 4.1m)

sample839.0ms

Algorithm
intervals
Results
348.0ms66×body2560valid
254.0ms82×body1280valid
137.0ms67×body640valid
17.0ms19×body320valid
10.0ms16×body160valid
2.0ms6×body80valid

simplify48.0ms

Calls
1 calls:
Slowest
47.0ms
(/ (- x (sin x)) (- x (tan x)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize62.0ms

Local error

Found 3 expressions with local error:

1.8b
(- x (sin x))
1.8b
(- x (tan x))
0.0b
(/ (- x (sin x)) (- x (tan x)))

rewrite65.0ms

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
35.0ms
(/ (- x (sin x)) (- x (tan x)))
15.0ms
(- x (sin x))
9.0ms
(- x (tan x))

series252.0ms

Calls
3 calls:
Slowest
108.0ms
(/ (- x (sin x)) (- x (tan x)))
82.0ms
(- x (tan x))
62.0ms
(- x (sin x))

simplify5.9s

Calls
122 calls:
Slowest
448.0ms
(- (+ 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)))))
438.0ms
(- (+ 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))))
340.0ms
(- (+ (* 1/3 (pow x 3)) (+ (* 2/15 (pow x 5)) (* 17/315 (pow x 7)))))
271.0ms
(- (+ (* 1/6 (pow x 3)) (* 1/5040 (pow x 7))) (* 1/120 (pow x 5)))

prune946.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

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))
0.1b
(fma -27/2800 (* (* x x) (* x x)) -1/2)

rewrite48.0ms

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
Calls
3 calls:
Slowest
45.0ms
(* (* x x) (* x x))
0.0ms
(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)

series242.0ms

Calls
3 calls:
Slowest
137.0ms
(fma -27/2800 (* (* x x) (* x x)) -1/2)
57.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
48.0ms
(* (* x x) (* x x))

simplify2.7s

Calls
76 calls:
Slowest
419.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
358.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
328.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
307.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
167.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune799.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

17.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
17.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
17.3b
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
5.5b
(cbrt (* (* (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
20.0ms
(cbrt (* (* (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
1.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
1.0ms
(fma (* x x) 9/40 (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))

series284.0ms

Calls
4 calls:
Slowest
79.0ms
(cbrt (* (* (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
78.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
66.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))
61.0ms
(fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify2.0s

Calls
14 calls:
Slowest
220.0ms
(cbrt (* (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2)) (fma (* x x) 9/40 (fma -27/2800 (* (* x x) (* x x)) -1/2))))
186.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
171.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
157.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
147.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

prune438.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.8b
(- x (tan x))
1.8b
(- x (tan x))
0.1b
(/ (sin x) (- x (tan x)))

rewrite147.0ms

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
Calls
4 calls:
Slowest
84.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
23.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
5.0ms
(- x (tan x))

series459.0ms

Calls
4 calls:
Slowest
269.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
75.0ms
(/ (sin x) (- x (tan x)))
59.0ms
(- x (tan x))
57.0ms
(- x (tan x))

simplify3.4m

Calls
1036 calls:
Slowest
736.0ms
(fma (* (cbrt (/ x (- x (tan x)))) (cbrt (/ x (- x (tan x))))) (cbrt (/ x (- x (tan x)))) (- (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
654.0ms
(fma (- (/ (cbrt (sin x)) (- x (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (- x (tan x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))
653.0ms
(fma (/ 1 (* (cbrt (- x (tan x))) (cbrt (- x (tan x))))) (/ x (cbrt (- x (tan x)))) (- (* (/ (sqrt (sin x)) (- x (tan x))) (/ (sqrt (sin x)) 1))))
643.0ms
(fma (- (/ (cbrt (sin x)) (- (sqrt x) (sqrt (tan x))))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (+ (sqrt x) (sqrt (tan x)))) (* (/ (cbrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (+ (sqrt x) (sqrt (tan x))))))
616.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (- x (tan x))) (- (* (/ (cbrt (sin x)) (- (sqrt x) (sqrt (tan x)))) (/ (* (cbrt (sin x)) (cbrt (sin x))) (+ (sqrt x) (sqrt (tan x)))))))

prune5.9s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch149.0ms

end0.0ms

sample15.6s

Algorithm
intervals
Results
6.4s1606×body2560valid
5.1s2698×body1280valid
2.5s1891×body640valid
1.1s963×body320valid
230.0ms447×body160valid
95.0ms395×body80valid