Details

Time bar (total: 19.3s)

sample150.0ms

Algorithm
intervals
Results
66.0ms73×body1280valid
38.0ms59×body640valid
20.0ms26×body2560valid
8.0ms20×body320valid
6.0ms62×body80valid
4.0ms16×body160valid

simplify11.0ms

Calls
1 calls:
Slowest
11.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.3b

localize9.0ms

Local error

Found 3 expressions with local error:

3.2b
(log (+ x (hypot 1 x)))
1.1b
(+ 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)

series164.0ms

Calls
3 calls:
Slowest
105.0ms
(log (+ x (hypot 1 x)))
38.0ms
(+ x (hypot 1 x))
21.0ms
(hypot 1 x)

simplify1.9s

Calls
15 calls:
Slowest
256.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
254.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
218.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
216.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
207.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

14.9b
(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
3.0ms
(* x -1/6)
3.0ms
(* (* x -1/6) x)
0.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series142.0ms

Calls
4 calls:
Slowest
78.0ms
(fma 3/40 (pow x 5) x)
33.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
19.0ms
(* (* x -1/6) x)
11.0ms
(* x -1/6)

simplify502.0ms

Calls
12 calls:
Slowest
143.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
143.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
130.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
12.0ms
(* -1/6 (pow x 2))
12.0ms
(+ x (* 3/40 (pow x 5)))

prune490.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

19.5b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
12.6b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
0.5b
(/ -1/8 (* x (* x x)))
0.2b
(/ 1/16 (pow x 5))

rewrite42.0ms

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
26.0ms
(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)))
1.0ms
(/ -1/8 (* x (* x x)))
1.0ms
(/ 1/16 (pow x 5))

series211.0ms

Calls
4 calls:
Slowest
92.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
64.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
32.0ms
(/ 1/16 (pow x 5))
24.0ms
(/ -1/8 (* x (* x x)))

simplify3.5s

Calls
34 calls:
Slowest
486.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
390.0ms
(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))))))
330.0ms
(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)))))
314.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))
238.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))

prune776.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

19.5b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
19.5b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
19.5b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
12.6b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×fma-def
10×add-sqr-sqrt add-log-exp
8×add-cube-cbrt
6×log-prod
5×pow1 log-div add-exp-log
4×expm1-log1p-u flip3-+ add-cbrt-cube frac-add flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
3×+-commutative sum-log frac-sub div-inv
2×distribute-lft-out--
1×flip3-- rem-log-exp log-pow flip-- difference-of-squares
Calls
4 calls:
Slowest
21.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
10.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
9.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
8.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))

series279.0ms

Calls
4 calls:
Slowest
103.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
65.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
57.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
54.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))

simplify4.7s

Calls
42 calls:
Slowest
513.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
422.0ms
(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))))))
348.0ms
(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)))))
239.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))
235.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.7% (0.1b remaining)

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

bsearch133.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.9s2383×body1280valid
1.2s1561×body640valid
507.0ms785×body2560valid
280.0ms761×body320valid
184.0ms2126×body80valid
105.0ms384×body160valid