Details

Time bar (total: 17.0s)

sample121.0ms

Algorithm
intervals
Results
66.0ms80×body1280valid
21.0ms49×body640valid
15.0ms26×body2560valid
6.0ms77×body80valid
4.0ms16×body320valid
1.0ms8×body160valid

simplify15.0ms

Calls
1 calls:
Slowest
15.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize15.0ms

Local error

Found 3 expressions with local error:

2.4b
(log (+ x (hypot 1 x)))
0.5b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite4.0ms

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
2.0ms
(log (+ x (hypot 1 x)))
1.0ms
(+ x (hypot 1 x))
0.0ms
(hypot 1 x)

series697.0ms

Calls
3 calls:
Slowest
570.0ms
(log (+ x (hypot 1 x)))
81.0ms
(+ x (hypot 1 x))
47.0ms
(hypot 1 x)

simplify1.9s

Calls
15 calls:
Slowest
260.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
259.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
248.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
192.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
178.0ms
(log (- (* x x) (* (hypot 1 x) (hypot 1 x))))

prune399.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

15.7b
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
0.4b
(* x -1/6)
0.1b
(* (* x -1/6) x)
0.0b
(fma 3/40 (pow x 5) x)

rewrite6.0ms

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
4.0ms
(* (* x -1/6) x)
0.0ms
(* x -1/6)
0.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series319.0ms

Calls
4 calls:
Slowest
173.0ms
(fma 3/40 (pow x 5) x)
78.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
42.0ms
(* (* x -1/6) x)
25.0ms
(* x -1/6)

simplify609.0ms

Calls
12 calls:
Slowest
185.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
161.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
147.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
17.0ms
(* -1/6 (pow x 2))
17.0ms
(* -1/6 (pow x 2))

prune540.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

12.4b
(log (fma 2 x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
0.3b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
3×log-prod
2×div-inv
1×pow2 +-commutative clear-num associate-/r* sum-log frac-2neg flip3-+ pow-plus rem-log-exp associate-*l* pow3 frac-add log-pow *-commutative flip-+ distribute-lft-out
Calls
4 calls:
Slowest
17.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
6.0ms
(* (* x x) x)
2.0ms
(log (fma 2 x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
2.0ms
(/ -1/8 (* (* x x) x))

series308.0ms

Calls
4 calls:
Slowest
112.0ms
(log (fma 2 x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
106.0ms
(+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))
55.0ms
(/ -1/8 (* (* x x) x))
35.0ms
(* (* x x) x)

simplify1.7s

Calls
22 calls:
Slowest
355.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
323.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))
186.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
111.0ms
(- (* 1/2 (/ 1 x)) (* 1/8 (/ 1 (pow x 3))))
104.0ms
(- (* 1/2 (/ 1 x)) (* 1/8 (/ 1 (pow x 3))))

prune735.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

20.0b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
14.6b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
0.3b
(/ -1/8 (* x (* x x)))
0.1b
(* x (* x x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
8×add-sqr-sqrt
6×log-prod add-cube-cbrt add-log-exp
5×pow1 log-div add-exp-log
4×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
3×frac-sub
2×flip3-+ frac-add flip-+ div-inv distribute-lft-out distribute-lft-out--
1×+-commutative clear-num associate-/r* sum-log frac-2neg flip3-- cube-unmult rem-log-exp associate-*r* log-pow *-commutative flip-- difference-of-squares
Calls
4 calls:
Slowest
23.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
14.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
2.0ms
(* x (* x x))
1.0ms
(/ -1/8 (* x (* x x)))

series398.0ms

Calls
4 calls:
Slowest
174.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
130.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
55.0ms
(/ -1/8 (* x (* x x)))
38.0ms
(* x (* x x))

simplify3.5s

Calls
31 calls:
Slowest
543.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
478.0ms
(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))))))
351.0ms
(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)))))
257.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
245.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))

prune745.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.9b

bsearch102.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s2369×body1280valid
920.0ms1606×body640valid
880.0ms805×body2560valid
267.0ms748×body320valid
250.0ms2078×body80valid
76.0ms394×body160valid