Details

Time bar (total: 26.4s)

sample493.0ms

Algorithm
intervals
Results
310.0ms103×body2560valid
114.0ms80×body1280valid
26.0ms35×body640valid
14.0ms22×body320valid
10.0ms256×pre80true
5.0ms13×body160valid
1.0ms3×body80valid

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(- (/ 1 x) (/ 1 (tan x)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize10.0ms

Local error

Found 2 expressions with local error:

3.3b
(- (/ 1 x) (/ 1 (tan x)))
0.0b
(/ 1 (tan x))

rewrite7.0ms

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
5.0ms
(- (/ 1 x) (/ 1 (tan x)))
1.0ms
(/ 1 (tan x))

series124.0ms

Calls
2 calls:
Slowest
96.0ms
(- (/ 1 x) (/ 1 (tan x)))
29.0ms
(/ 1 (tan x))

simplify3.1s

Calls
62 calls:
Slowest
338.0ms
(- (/ 1 x) (+ (* 1/3 x) (* 1/45 (pow x 3))))
129.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
121.0ms
(fma 1 (/ 1 x) (- (* (cos x) (/ 1 (sin x)))))
119.0ms
(fma (* (cbrt (/ 1 x)) (cbrt (/ 1 x))) (cbrt (/ 1 x)) (- (* (cos x) (/ 1 (sin x)))))
113.0ms
(fma (- (cos x)) (/ 1 (sin x)) (* (cos x) (/ 1 (sin x))))

prune469.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (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))

rewrite4.0ms

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
3.0ms
(* (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))

series103.0ms

Calls
3 calls:
Slowest
43.0ms
(fma 2/945 (pow x 5) (* (fma 1/45 (* x x) 1/3) x))
38.0ms
(* (fma 1/45 (* x x) 1/3) x)
22.0ms
(fma 1/45 (* x x) 1/3)

simplify705.0ms

Calls
11 calls:
Slowest
154.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
140.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
133.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
72.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
53.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune447.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
0.0b
(log (exp (fma 1/45 (* x x) 1/3)))
0.0b
(fma 1/45 (* x x) 1/3)
0.0b
(fma 2/945 (pow x 5) (* (log (exp (fma 1/45 (* x x) 1/3))) x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity log-pow add-cube-cbrt
7×associate-*l*
6×pow1 exp-prod
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×rem-log-exp exp-sum *-commutative
Calls
4 calls:
Slowest
7.0ms
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
2.0ms
(log (exp (fma 1/45 (* x x) 1/3)))
0.0ms
(fma 1/45 (* x x) 1/3)
0.0ms
(fma 2/945 (pow x 5) (* (log (exp (fma 1/45 (* x x) 1/3))) x))

series158.0ms

Calls
4 calls:
Slowest
41.0ms
(log (exp (fma 1/45 (* x x) 1/3)))
41.0ms
(* (log (exp (fma 1/45 (* x x) 1/3))) x)
40.0ms
(fma 2/945 (pow x 5) (* (log (exp (fma 1/45 (* x x) 1/3))) x))
36.0ms
(fma 1/45 (* x x) 1/3)

simplify1.1s

Calls
24 calls:
Slowest
152.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
120.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
109.0ms
(+ (* 1/3 x) (+ (* 1/45 (pow x 3)) (* 2/945 (pow x 5))))
77.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))
74.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune854.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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)

rewrite25.0ms

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
20.0ms
(* (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)

series167.0ms

Calls
4 calls:
Slowest
79.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) x)
39.0ms
(* (sqrt (fma 1/45 (* x x) 1/3)) (* (sqrt (fma 1/45 (* x x) 1/3)) x))
29.0ms
(fma 1/45 (* x x) 1/3)
21.0ms
(fma 1/45 (* x x) 1/3)

simplify2.1s

Calls
25 calls:
Slowest
453.0ms
(* (* (* (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)))
367.0ms
(- (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))) (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))))
338.0ms
(- (+ (* x (sqrt 1/3)) (* 1/90 (/ (pow x 3) (sqrt 1/3)))) (* 1/16200 (/ (pow x 5) (pow (sqrt 1/3) 3))))
251.0ms
(- (* 1/72 (/ 1 (* (pow x 2) (pow (sqrt 1/45) 3)))) (+ (* (pow x 2) (sqrt 1/45)) (* 1/6 (/ 1 (sqrt 1/45)))))
80.0ms
(+ (* 1/3 x) (* 1/45 (pow x 3)))

prune739.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample15.6s

Algorithm
intervals
Results
9.2s3275×body2560valid
3.6s2536×body1280valid
1.7s1228×body640valid
418.0ms606×body320valid
298.0ms8000×pre80true
112.0ms310×body160valid
8.0ms45×body80valid