Details

Time bar (total: 17.7s)

sample150.0ms

Algorithm
intervals
Results
71.0ms75×body1280valid
29.0ms48×body640valid
24.0ms34×body2560valid
9.0ms25×body320valid
5.0ms61×body80valid
3.0ms13×body160valid

simplify14.0ms

Calls
1 calls:
Slowest
14.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize18.0ms

Local error

Found 3 expressions with local error:

3.0b
(log (+ x (hypot 1 x)))
0.8b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite6.0ms

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
3.0ms
(log (+ x (hypot 1 x)))
2.0ms
(+ x (hypot 1 x))
0.0ms
(hypot 1 x)

series227.0ms

Calls
3 calls:
Slowest
156.0ms
(log (+ x (hypot 1 x)))
36.0ms
(hypot 1 x)
35.0ms
(+ x (hypot 1 x))

simplify2.0s

Calls
15 calls:
Slowest
292.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
285.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
210.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
196.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
190.0ms
(log (- (* x x) (* (hypot 1 x) (hypot 1 x))))

prune424.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

17.3b
(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)

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
(* 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)

series126.0ms

Calls
4 calls:
Slowest
57.0ms
(fma 3/40 (pow x 5) x)
44.0ms
(fma (* (* x -1/6) x) x (fma 3/40 (pow x 5) x))
15.0ms
(* (* x -1/6) x)
11.0ms
(* x -1/6)

simplify555.0ms

Calls
12 calls:
Slowest
151.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
150.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
144.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
21.0ms
(* -1/6 (pow x 2))
16.0ms
(+ x (* 3/40 (pow x 5)))

prune474.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

19.2b
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
13.9b
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
0.3b
(/ -1/8 (* x (* x x)))
0.2b
(/ 1/16 (pow x 5))

rewrite57.0ms

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
39.0ms
(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)))
0.0ms
(/ 1/16 (pow x 5))

series161.0ms

Calls
4 calls:
Slowest
76.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))))
52.0ms
(+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5)))
18.0ms
(/ 1/16 (pow x 5))
15.0ms
(/ -1/8 (* x (* x x)))

simplify3.1s

Calls
34 calls:
Slowest
497.0ms
(log (- (pow (/ -1/2 x) 3) (pow (+ (/ -1/8 (* x (* x x))) (/ 1/16 (pow x 5))) 3)))
450.0ms
(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))))))
308.0ms
(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)))))
221.0ms
(log (- (* -1/2 (* (* x (* x x)) (pow x 5))) (* x (+ (* -1/8 (pow x 5)) (* (* x (* x x)) 1/16)))))
195.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune762.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (+ x (hypot 1 x)))
3.0b
(log (+ x (hypot 1 x)))
3.0b
(log (+ x (hypot 1 x)))
0.8b
(+ x (hypot 1 x))

rewrite10.0ms

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

series410.0ms

Calls
4 calls:
Slowest
140.0ms
(log (+ x (hypot 1 x)))
122.0ms
(log (+ x (hypot 1 x)))
119.0ms
(log (+ x (hypot 1 x)))
29.0ms
(+ x (hypot 1 x))

simplify3.8s

Calls
30 calls:
Slowest
709.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
347.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
312.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
283.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
282.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))

prune607.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.6b

bsearch126.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.1s2388×body1280valid
881.0ms1613×body640valid
567.0ms2047×body80valid
534.0ms787×body2560valid
302.0ms768×body320valid
75.0ms397×body160valid