Details

Time bar (total: 30.4s)

sample447.0ms

Algorithm
intervals
Results
265.0ms90×body2560valid
115.0ms95×body1280valid
28.0ms37×body640valid
12.0ms22×body320valid
10.0ms256×pre80true
4.0ms11×body160valid
0.0ms1×body80valid

simplify66.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize21.0ms

Local error

Found 2 expressions with local error:

3.2b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
20×prod-diff
17×*-un-lft-identity
15×add-sqr-sqrt div-inv
13×add-cube-cbrt
5×tan-quot associate-/r/
4×fma-neg distribute-lft-out-- add-log-exp
3×pow1 associate-/r* add-exp-log
2×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
1×rec-exp clear-num sub-neg frac-2neg flip3-- diff-log frac-sub pow-flip flip-- inv-pow difference-of-squares
Calls
2 calls:
Slowest
7.0ms
(- (/ 1 x) (/ 1 (tan x)))
1.0ms
(/ 1 (tan x))

series99.0ms

Calls
2 calls:
Slowest
66.0ms
(- (/ 1 x) (/ 1 (tan x)))
33.0ms
(/ 1 (tan x))

simplify3.2s

Calls
62 calls:
Slowest
405.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
119.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
110.0ms
(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))
104.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
93.0ms
(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))

prune558.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (fma 1/45 (* x x) 1/3) x)
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u pow1 add-cbrt-cube associate-*l* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×*-commutative
Calls
3 calls:
Slowest
6.0ms
(* (fma 1/45 (* x x) 1/3) x)
0.0ms
(fma 1/45 (* x x) 1/3)
0.0ms
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))

series124.0ms

Calls
3 calls:
Slowest
45.0ms
(* (fma 1/45 (* x x) 1/3) x)
42.0ms
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))
37.0ms
(fma 1/45 (* x x) 1/3)

simplify695.0ms

Calls
11 calls:
Slowest
138.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
125.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
125.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
64.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
62.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune416.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma 1/45 (* x x) 1/3)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l*
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative fma-udef
1×associate-*r* pow-prod-down prod-exp cbrt-unprod
Calls
4 calls:
Slowest
11.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
3.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
0.0ms
(fma 1/45 (* x x) 1/3)
0.0ms
(fma 1/45 (* x x) 1/3)

series151.0ms

Calls
4 calls:
Slowest
61.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
37.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
28.0ms
(fma 1/45 (* x x) 1/3)
24.0ms
(fma 1/45 (* x x) 1/3)

simplify2.0s

Calls
25 calls:
Slowest
536.0ms
(* (* (* (sqrt (fma 1/45 (* x x) 1/3)) (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (fma 1/45 (* x x) 1/3))) (* (* (* (sqrt (fma 1/45 (* x x) 1/3)) x) (* (sqrt (fma 1/45 (* x x) 1/3)) x)) (* (sqrt (fma 1/45 (* x x) 1/3)) x)))
306.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
296.0ms
(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
258.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
50.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune873.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
0.3b
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
0.1b
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
0.0b
(fma 1/45 (* x x) 1/3)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*l*
21×sqrt-prod
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×associate-*r*
1×fma-udef
Calls
4 calls:
Slowest
32.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
13.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
4.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
0.0ms
(fma 1/45 (* x x) 1/3)

series343.0ms

Calls
4 calls:
Slowest
201.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
65.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
51.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))
26.0ms
(fma 1/45 (* x x) 1/3)

simplify3.5s

Calls
43 calls:
Slowest
349.0ms
(- (+ (* x (pow 1/3 1/4)) (* 1/60 (* (pow x 3) (pow 1/3 1/4)))) (* 1/2400 (* (pow x 5) (pow 1/3 1/4))))
341.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
336.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
305.0ms
(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
294.0ms
(* (* (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (sqrt (sqrt (fma 1/45 (* x x) 1/3)))) (* (* (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample16.6s

Algorithm
intervals
Results
10.3s3279×body2560valid
4.1s2502×body1280valid
1.2s1238×body640valid
385.0ms653×body320valid
323.0ms8000×pre80true
105.0ms284×body160valid
8.0ms44×body80valid