Details

Time bar (total: 28.5s)

sample164.0ms

Algorithm
intervals
Results
86.0ms83×body1280valid
22.0ms39×body640valid
22.0ms28×body2560valid
12.0ms32×body320valid
6.0ms61×body80valid
3.0ms13×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.6b

localize16.0ms

Local error

Found 2 expressions with local error:

3.1b
(log (+ x (hypot 1 x)))
0.8b
(+ x (hypot 1 x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt pow1 log-prod *-un-lft-identity add-exp-log add-cube-cbrt
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u add-log-exp
1×+-commutative rem-log-exp log-pow
Calls
2 calls:
Slowest
3.0ms
(log (+ x (hypot 1 x)))
2.0ms
(+ x (hypot 1 x))

series691.0ms

Calls
2 calls:
Slowest
503.0ms
(+ x (hypot 1 x))
188.0ms
(log (+ x (hypot 1 x)))

simplify1.5s

Calls
12 calls:
Slowest
301.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
245.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
217.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
191.0ms
(log (- (* x x) (* (hypot 1 x) (hypot 1 x))))
184.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune283.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

14.1b
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.1b
(* (* x -1/6) x)
0.0b
(fma 3/40 (pow x 5) x)

rewrite4.0ms

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
2×*-commutative fma-udef
1×associate-*l*
Calls
4 calls:
Slowest
3.0ms
(* (* x -1/6) x)
0.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
0.0ms
(* x -1/6)
0.0ms
(fma 3/40 (pow x 5) x)

series324.0ms

Calls
4 calls:
Slowest
167.0ms
(fma 3/40 (pow x 5) x)
90.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
40.0ms
(* (* x -1/6) x)
27.0ms
(* x -1/6)

simplify585.0ms

Calls
12 calls:
Slowest
210.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
162.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
149.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
10.0ms
(+ x (* 3/40 (pow x 5)))
9.0ms
(+ x (* 3/40 (pow x 5)))

prune545.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

18.6b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
12.9b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
0.3b
(/ 1/16 (pow x 5))
0.2b
(/ -1/8 (* x (* x x)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
7×add-cube-cbrt
6×log-prod add-log-exp
5×pow1 log-div add-exp-log
4×expm1-log1p-u associate-/r* fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
3×frac-sub div-inv
2×clear-num frac-2neg flip3-+ frac-add flip-+ distribute-lft-out distribute-lft-out--
1×+-commutative sum-log flip3-- rem-log-exp log-pow flip-- difference-of-squares
Calls
4 calls:
Slowest
34.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
8.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
1.0ms
(/ -1/8 (* x (* x x)))
1.0ms
(/ 1/16 (pow x 5))

series487.0ms

Calls
4 calls:
Slowest
222.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
153.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
59.0ms
(/ 1/16 (pow x 5))
52.0ms
(/ -1/8 (* x (* x x)))

simplify3.6s

Calls
34 calls:
Slowest
514.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
437.0ms
(log (- (* (/ -1/2 x) (/ -1/2 x)) (* (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))))))
370.0ms
(log (- (* -1/2 (+ (* (/ -1/8 (* x (* x x))) (/ -1/8 (* x (* x x)))) (- (* (/ 1/16 (pow x 5)) (/ 1/16 (pow x 5))) (* (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))) (* x (+ (pow (/ -1/8 (* x (* x x))) 3) (pow (/ 1/16 (pow x 5)) 3)))))
268.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))
238.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune686.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

11.9b
(+ (pow x 3) (pow (hypot 1 x) 3))
9.0b
(/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
7.9b
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))
3.1b
(log (/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
30×times-frac
24×add-sqr-sqrt add-cube-cbrt
21×log-prod
9×add-exp-log
8×sum-cubes distribute-lft-out add-log-exp
6×add-cbrt-cube
5×pow1 fma-def associate-/l*
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ insert-posit16 log1p-expm1-u
3×associate-/r*
2×div-exp rem-log-exp div-inv associate-/l/
1×cube-mult cbrt-undiv +-commutative log-div clear-num sum-log sub-neg frac-2neg flip3-- distribute-rgt-out-- fma-neg diff-log unpow3 prod-diff log-pow flip--
Calls
4 calls:
Slowest
40.0ms
(/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
15.0ms
(log (/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))
11.0ms
(+ (pow x 3) (pow (hypot 1 x) 3))
7.0ms
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))

series1.1s

Calls
4 calls:
Slowest
481.0ms
(log (/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))
316.0ms
(/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))
186.0ms
(- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))
114.0ms
(+ (pow x 3) (pow (hypot 1 x) 3))

simplify12.1s

Calls
91 calls:
Slowest
477.0ms
(/ (* (* (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (pow x 3) (pow (hypot 1 x) 3))) (+ (pow x 3) (pow (hypot 1 x) 3))) (* (* (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))) (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))
465.0ms
(log (/ (+ (pow x 3) (pow (hypot 1 x) 3)) (+ (pow (* x x) 3) (pow (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))) 3))))
387.0ms
(log (/ (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))) (* (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))) (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))))
380.0ms
(log (/ (* (cbrt (+ (pow x 3) (pow (hypot 1 x) 3))) (cbrt (+ (pow x 3) (pow (hypot 1 x) 3)))) (* (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))) (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))))))
296.0ms
(/ (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))) (* (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x))))) (cbrt (+ (* x x) (- (* (hypot 1 x) (hypot 1 x)) (* x (hypot 1 x)))))))

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch129.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.5s2433×body1280valid
804.0ms1476×body640valid
558.0ms794×body2560valid
311.0ms805×body320valid
164.0ms2109×body80valid
72.0ms383×body160valid