Details

Time bar (total: 17.2s)

sample118.0ms

Algorithm
intervals
Results
54.0ms76×body1280valid
21.0ms46×body640valid
18.0ms31×body2560valid
6.0ms21×body320valid
5.0ms70×body80valid
2.0ms12×body160valid

simplify21.0ms

Calls
1 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize10.0ms

Local error

Found 3 expressions with local error:

3.3b
(log (+ x (hypot 1 x)))
0.6b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-exp-log add-cube-cbrt
3×expm1-log1p-u log-prod add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×log-div flip3-+ flip-+
1×+-commutative hypot-udef rem-log-exp log-pow
Calls
3 calls:
Slowest
1.0ms
(log (+ x (hypot 1 x)))
1.0ms
(+ x (hypot 1 x))
0.0ms
(hypot 1 x)

series216.0ms

Calls
3 calls:
Slowest
138.0ms
(log (+ x (hypot 1 x)))
44.0ms
(+ x (hypot 1 x))
34.0ms
(hypot 1 x)

simplify1.8s

Calls
15 calls:
Slowest
280.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
234.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
227.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
178.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
172.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune458.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

16.6b
(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)

rewrite7.0ms

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
5.0ms
(* (* 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)

series120.0ms

Calls
4 calls:
Slowest
59.0ms
(fma 3/40 (pow x 5) x)
38.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
12.0ms
(* x -1/6)
11.0ms
(* (* x -1/6) x)

simplify594.0ms

Calls
12 calls:
Slowest
188.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
153.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
145.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
20.0ms
(+ x (* 3/40 (pow x 5)))
16.0ms
(* -1/6 (pow x 2))

prune525.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))
0.6b
(+ x (hypot 1 x))
0.6b
(+ x (hypot 1 x))
0.2b
(sqrt (+ x (hypot 1 x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-div
10×pow1
9×flip3-+ flip-+
8×log-div
7×add-exp-log log-pow
6×add-sqr-sqrt
5×*-un-lft-identity pow1/2 add-cube-cbrt
4×expm1-log1p-u frac-times add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×+-commutative rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 rem-sqrt-square log-prod pow-plus prod-exp
Calls
4 calls:
Slowest
15.0ms
(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))
2.0ms
(sqrt (+ x (hypot 1 x)))
2.0ms
(+ x (hypot 1 x))
2.0ms
(+ x (hypot 1 x))

series265.0ms

Calls
4 calls:
Slowest
136.0ms
(log (* (sqrt (+ x (hypot 1 x))) (sqrt (+ x (hypot 1 x)))))
47.0ms
(sqrt (+ x (hypot 1 x)))
45.0ms
(+ x (hypot 1 x))
37.0ms
(+ x (hypot 1 x))

simplify2.9s

Calls
32 calls:
Slowest
250.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
244.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
233.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
221.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
209.0ms
(log (* (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))) (sqrt (- (* x x) (* (hypot 1 x) (hypot 1 x))))))

prune744.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

18.1b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
10.2b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
0.3b
(/ -1/8 (* x (* x x)))
0.1b
(/ 1/16 (pow x 5))

rewrite61.0ms

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
41.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
16.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
1.0ms
(/ -1/8 (* x (* x x)))
1.0ms
(/ 1/16 (pow x 5))

series230.0ms

Calls
4 calls:
Slowest
111.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
63.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
31.0ms
(/ 1/16 (pow x 5))
24.0ms
(/ -1/8 (* x (* x x)))

simplify3.5s

Calls
34 calls:
Slowest
480.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
415.0ms
(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))))))
324.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))
310.0ms
(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)))))
288.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune815.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.1b

bsearch106.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.3s2325×body1280valid
889.0ms1565×body640valid
594.0ms800×body2560valid
301.0ms755×body320valid
201.0ms2137×body80valid
122.0ms418×body160valid