Details

Time bar (total: 22.1s)

sample155.0ms

Algorithm
intervals
Results
69.0ms77×body1280valid
31.0ms52×body640valid
28.0ms22×body2560valid
9.0ms25×body320valid
6.0ms71×body80valid
2.0ms9×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize9.0ms

Local error

Found 3 expressions with local error:

2.1b
(log (+ x (hypot 1 x)))
0.5b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Counts
3 → 47
Calls
3 calls:
Slowest
6.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series376.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
216.0ms
(log (+ x (hypot 1 x)))
83.0ms
(+ x (hypot 1 x))
76.0ms
(hypot 1 x)

simplify2.7s

Counts
20 → 56
Calls
20 calls:
Slowest
362.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
351.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
340.0ms
(- (+ (* 1/2 (pow x 2)) 1) (* 1/8 (pow x 4)))
273.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
240.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune497.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

14.6b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.1b
(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)

series279.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
176.0ms
(fma 3/40 (pow x 5) x)
75.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
27.0ms
(* x -1/6)

simplify1.3s

Counts
18 → 52
Calls
18 calls:
Slowest
198.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
197.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
182.0ms
(+ x (* 3/40 (pow x 5)))
179.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
172.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))

prune504.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b
(log (+ x (hypot 1 x)))
2.1b
(log (+ x (hypot 1 x)))
2.1b
(log (+ x (hypot 1 x)))
0.5b
(+ x (hypot 1 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×log-prod
8×add-sqr-sqrt add-cube-cbrt
7×pow1 add-exp-log
6×log-div add-log-exp
4×expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def rem-log-exp log-pow
1×+-commutative sum-log
Counts
4 → 72
Calls
4 calls:
Slowest
7.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))
3.0ms
(log (+ x (hypot 1 x)))
3.0ms
(log (+ x (hypot 1 x)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
214.0ms
(log (+ x (hypot 1 x)))
204.0ms
(log (+ x (hypot 1 x)))
192.0ms
(log (+ x (hypot 1 x)))
99.0ms
(+ x (hypot 1 x))

simplify4.1s

Counts
37 → 84
Calls
37 calls:
Slowest
378.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
355.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
344.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
289.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
261.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune691.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

11.1b
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))
2.1b
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
0.3b
(cbrt (hypot 1 x))
0.3b
(cbrt (hypot 1 x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×log-prod fma-def
2×log-div flip3-+ pow1/3 flip-+
1×+-commutative sum-log rem-log-exp log-pow
Counts
4 → 62
Calls
4 calls:
Slowest
11.0ms
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))
5.0ms
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
1.0ms
(cbrt (hypot 1 x))
1.0ms
(cbrt (hypot 1 x))

series927.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
437.0ms
(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))
181.0ms
(cbrt (hypot 1 x))
159.0ms
(cbrt (hypot 1 x))
150.0ms
(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))

simplify4.1s

Counts
27 → 74
Calls
27 calls:
Slowest
381.0ms
(- (+ (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))))
310.0ms
(- (+ (* 1/6 (pow x 2)) 1) (* 5/72 (pow x 4)))
295.0ms
(* (exp x) (exp (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
279.0ms
(- (+ (* 1/6 (pow x 2)) 1) (* 5/72 (pow x 4)))

prune679.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.2b

bsearch129.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.1s2333×body1280valid
880.0ms1552×body640valid
695.0ms2114×body80valid
582.0ms835×body2560valid
286.0ms772×body320valid
79.0ms394×body160valid