Details

Time bar (total: 25.2s)

sample97.0ms

Algorithm
intervals
Results
43.0ms73×body1280valid
20.0ms53×body640valid
15.0ms24×body2560valid
6.0ms28×body320valid
4.0ms66×body80valid
2.0ms12×body160valid

simplify12.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize12.0ms

Local error

Found 3 expressions with local error:

4.2b
(log (+ x (hypot 1 x)))
0.2b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite17.0ms

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
9.0ms
(+ x (hypot 1 x))
7.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series354.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
231.0ms
(log (+ x (hypot 1 x)))
74.0ms
(+ x (hypot 1 x))
49.0ms
(hypot 1 x)

simplify2.3s

Counts
20 → 56
Calls
20 calls:
Slowest
304.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
286.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
238.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
233.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
232.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune531.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

13.9b
(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)

rewrite13.0ms

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
11.0ms
(* x -1/6)
1.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series265.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
156.0ms
(fma 3/40 (pow x 5) x)
82.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
27.0ms
(* x -1/6)

simplify1.0s

Counts
18 → 52
Calls
18 calls:
Slowest
199.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
168.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
150.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
132.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
122.0ms
(+ x (* 3/40 (pow x 5)))

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.2b
(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
0.2b
(+ x (hypot 1 x))
0.2b
(+ x (hypot 1 x))
0.2b
(+ x (hypot 1 x))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×log-div
24×pow1
15×log-pow
14×associate-*l/
13×*-un-lft-identity
10×add-exp-log add-log-exp
9×fma-def pow1/3 pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×+-commutative sum-log rem-log-exp prod-exp pow-sqr distribute-lft-out
2×pow2
1×log-prod pow3
Counts
4 → 109
Calls
4 calls:
Slowest
52.0ms
(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
8.0ms
(+ x (hypot 1 x))
5.0ms
(+ x (hypot 1 x))
4.0ms
(+ x (hypot 1 x))

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
98.0ms
(+ x (hypot 1 x))
73.0ms
(+ x (hypot 1 x))
73.0ms
(+ x (hypot 1 x))

simplify10.5s

Counts
64 → 121
Calls
64 calls:
Slowest
393.0ms
(log (* (* (cbrt (+ (pow x 3) (pow (hypot 1 x) 3))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ (pow x 3) (pow (hypot 1 x) 3)))))
383.0ms
(log (* (* (cbrt (+ (pow x 3) (pow (hypot 1 x) 3))) (cbrt (+ (pow x 3) (pow (hypot 1 x) 3)))) (cbrt (+ x (hypot 1 x)))))
383.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
377.0ms
(log (* (* (cbrt (+ (pow x 3) (pow (hypot 1 x) 3))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))
363.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

4.2b
(log (+ x (hypot 1 x)))
0.2b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite9.0ms

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
5.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))
0.0ms
(hypot 1 x)

series370.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
214.0ms
(log (+ x (hypot 1 x)))
92.0ms
(+ x (hypot 1 x))
64.0ms
(hypot 1 x)

simplify2.2s

Counts
20 → 56
Calls
20 calls:
Slowest
297.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
286.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
241.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
233.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
211.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune471.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch129.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.6s2324×body1280valid
832.0ms1591×body640valid
653.0ms809×body2560valid
344.0ms787×body320valid
218.0ms2145×body80valid
69.0ms344×body160valid