Details

Time bar (total: 29.9s)

sample408.0ms

Algorithm
intervals
Results
241.0ms96×body2560valid
101.0ms83×body1280valid
28.0ms41×body640valid
12.0ms24×body320valid
10.0ms256×pre80true
4.0ms11×body160valid
0.0ms1×body80valid

simplify47.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.1b

localize12.0ms

Local error

Found 2 expressions with local error:

3.4b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite8.0ms

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
6.0ms
(- (/ 1 x) (/ 1 (tan x)))
1.0ms
(/ 1 (tan x))

series101.0ms

Calls
2 calls:
Slowest
68.0ms
(- (/ 1 x) (/ 1 (tan x)))
33.0ms
(/ 1 (tan x))

simplify3.0s

Calls
62 calls:
Slowest
380.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
134.0ms
(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))
123.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
117.0ms
(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))
107.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))

prune487.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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

series74.0ms

Calls
2 calls:
Slowest
42.0ms
(* (fma 1/45 (* x x) 1/3) x)
32.0ms
(fma 1/45 (* x x) 1/3)

simplify326.0ms

Calls
8 calls:
Slowest
64.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
62.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
51.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
33.0ms
(+ (* 1/45 (pow x 2)) 1/3)
33.0ms
(* (cbrt (fma 1/45 (* x x) 1/3)) (cbrt (fma 1/45 (* x x) 1/3)))

prune340.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

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)

rewrite26.0ms

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
18.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
6.0ms
(* (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)

series170.0ms

Calls
4 calls:
Slowest
64.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
54.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
30.0ms
(fma 1/45 (* x x) 1/3)
21.0ms
(fma 1/45 (* x x) 1/3)

simplify1.8s

Calls
25 calls:
Slowest
403.0ms
(* (* (* (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)))
288.0ms
(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
275.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
262.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
77.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune753.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
31×sqrt-prod
24×associate-*l*
16×add-sqr-sqrt
14×*-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×rem-sqrt-square associate-*r*
1×pow1/2
Calls
4 calls:
Slowest
35.0ms
(* (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)))
17.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
5.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
3.0ms
(sqrt (sqrt (fma 1/45 (* x x) 1/3)))

series401.0ms

Calls
4 calls:
Slowest
168.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x)
139.0ms
(sqrt (sqrt (fma 1/45 (* x x) 1/3)))
54.0ms
(* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) (* (sqrt (sqrt (fma 1/45 (* x x) 1/3))) x))
39.0ms
(* (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)))

simplify4.6s

Calls
51 calls:
Slowest
424.0ms
(- (+ (* 15/4 (/ (exp (* 1/4 (- (log 1/45) (* 2 (log (/ 1 x)))))) (pow x 2))) (exp (* 1/4 (- (log 1/45) (* 2 (log (/ 1 x))))))) (* 675/32 (/ (exp (* 1/4 (- (log 1/45) (* 2 (log (/ 1 x)))))) (pow x 4))))
363.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
358.0ms
(- (+ (* 1/60 (* (pow x 2) (pow 1/3 1/4))) (pow 1/3 1/4)) (* 1/2400 (* (pow x 4) (pow 1/3 1/4))))
340.0ms
(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
312.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))

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 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample15.8s

Algorithm
intervals
Results
9.4s3247×body2560valid
3.4s2484×body1280valid
1.1s8000×pre80true
1.1s1259×body640valid
379.0ms670×body320valid
178.0ms293×body160valid
8.0ms47×body80valid