Details

Time bar (total: 21.0s)

sample121.0ms

Algorithm
intervals
Results
55.0ms68×body1280valid
26.0ms54×body640valid
16.0ms24×body2560valid
7.0ms23×body320valid
7.0ms80×body80valid
1.0ms7×body160valid

simplify12.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt log-prod add-cube-cbrt add-log-exp
3×pow1 fma-def add-exp-log
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Counts
2 → 36
Calls
2 calls:
Slowest
9.0ms
(+ x (hypot 1 x))
7.0ms
(log (+ x (hypot 1 x)))

series281.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
205.0ms
(log (+ x (hypot 1 x)))
76.0ms
(+ x (hypot 1 x))

simplify1.7s

Counts
17 → 42
Calls
17 calls:
Slowest
342.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
333.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
207.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
201.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
169.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune343.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

17.6b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.0b
(fma 3/40 (pow x 5) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
5.0ms
(* 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)

series295.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
181.0ms
(fma 3/40 (pow x 5) x)
94.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
19.0ms
(* x -1/6)

simplify1.2s

Counts
18 → 52
Calls
18 calls:
Slowest
225.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
173.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
173.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
165.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
160.0ms
(+ x (* 3/40 (pow x 5)))

prune415.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (+ x (hypot 1 x)))
0.4b
(exp (log (log (+ x (hypot 1 x)))))
0.0b
(log (log (+ x (hypot 1 x))))
0.0b
(+ x (hypot 1 x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×log-prod
9×add-sqr-sqrt pow1 add-cube-cbrt
6×add-exp-log add-log-exp
5×log-pow
4×expm1-log1p-u exp-prod add-cbrt-cube exp-sum insert-posit16 log1p-expm1-u
3×fma-def
2×log-div flip3-+ rem-log-exp flip-+ distribute-lft-out
1×+-commutative sum-log rem-exp-log
Counts
4 → 71
Calls
4 calls:
Slowest
9.0ms
(log (log (+ x (hypot 1 x))))
7.0ms
(log (+ x (hypot 1 x)))
6.0ms
(exp (log (log (+ x (hypot 1 x)))))
4.0ms
(+ x (hypot 1 x))

series640.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(log (log (+ x (hypot 1 x))))
173.0ms
(exp (log (log (+ x (hypot 1 x)))))
162.0ms
(log (+ x (hypot 1 x)))
80.0ms
(+ x (hypot 1 x))

simplify3.4s

Counts
37 → 83
Calls
37 calls:
Slowest
377.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
337.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
289.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
246.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
230.0ms
(- (+ (* 3/32 (/ 1 (* (pow x 4) (+ (log (/ -1 x)) (log 1/2))))) (log (+ (log (/ -1 x)) (log 1/2)))) (+ (* 1/32 (/ 1 (* (pow x 4) (pow (+ (log (/ -1 x)) (log 1/2)) 2)))) (* 1/4 (/ 1 (* (pow x 2) (+ (log (/ -1 x)) (log 1/2)))))))

prune770.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

3.0b
(log (+ x (hypot 1 x)))
0.4b
(pow E (log (log (+ x (hypot 1 x)))))
0.0b
(log (log (+ x (hypot 1 x))))
0.0b
(+ x (hypot 1 x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×log-prod
10×add-sqr-sqrt pow1 add-cube-cbrt
7×add-exp-log
6×add-log-exp
5×log-pow
4×expm1-log1p-u unpow-prod-up pow-unpow add-cbrt-cube insert-posit16 log1p-expm1-u
3×unpow-prod-down fma-def
2×log-div flip3-+ rem-log-exp pow-exp flip-+ distribute-lft-out
1×pow-to-exp +-commutative e-exp-1 sum-log pow-pow sqr-pow
Counts
4 → 78
Calls
4 calls:
Slowest
9.0ms
(+ x (hypot 1 x))
7.0ms
(log (log (+ x (hypot 1 x))))
7.0ms
(log (+ x (hypot 1 x)))
5.0ms
(pow E (log (log (+ x (hypot 1 x)))))

series917.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
372.0ms
(pow E (log (log (+ x (hypot 1 x)))))
267.0ms
(log (log (+ x (hypot 1 x))))
202.0ms
(log (+ x (hypot 1 x)))
75.0ms
(+ x (hypot 1 x))

simplify5.0s

Counts
41 → 90
Calls
41 calls:
Slowest
541.0ms
(log (- (* x x) (* (hypot 1 x) (hypot 1 x))))
369.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
327.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
276.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
266.0ms
(pow (sqrt E) (log (log (+ x (hypot 1 x)))))

prune869.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch127.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s2320×body1280valid
924.0ms1584×body640valid
576.0ms2135×body80valid
505.0ms740×body2560valid
259.0ms798×body320valid
85.0ms423×body160valid