Details

Time bar (total: 18.6s)

sample144.0ms

Algorithm
intervals
Results
78.0ms88×body1280valid
25.0ms46×body640valid
14.0ms22×body2560valid
6.0ms19×body320valid
6.0ms70×body80valid
2.0ms11×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize18.0ms

Local error

Found 3 expressions with local error:

2.6b
(log (+ x (hypot 1 x)))
0.8b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite14.0ms

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
7.0ms
(log (+ x (hypot 1 x)))
6.0ms
(+ x (hypot 1 x))
0.0ms
(hypot 1 x)

series358.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
185.0ms
(log (+ x (hypot 1 x)))
88.0ms
(+ x (hypot 1 x))
86.0ms
(hypot 1 x)

simplify2.2s

Counts
20 → 56
Calls
20 calls:
Slowest
295.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
252.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
244.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
223.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
200.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune506.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 3 expressions with local error:

13.6b
(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)

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)

series282.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
198.0ms
(fma 3/40 (pow x 5) x)
63.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
21.0ms
(* x -1/6)

simplify1.1s

Counts
18 → 52
Calls
18 calls:
Slowest
179.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
162.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
154.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
151.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
147.0ms
(+ x (* 3/40 (pow x 5)))

prune461.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

13.6b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
13.6b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
13.6b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
12.9b
(cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 47
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)))
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

series467.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)))
108.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
84.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
77.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

simplify3.0s

Counts
15 → 59
Calls
15 calls:
Slowest
490.0ms
(cbrt (* (cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))) (cbrt (fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x)))))
306.0ms
(- (+ (exp (* 1/3 (- (log -3/40) (* 5 (log (/ -1 x)))))) (* 2840/729 (/ (exp (* 1/3 (- (log -3/40) (* 5 (log (/ -1 x)))))) (pow x 4)))) (* 20/27 (/ (exp (* 1/3 (- (log -3/40) (* 5 (log (/ -1 x)))))) (pow x 2))))
299.0ms
(- (+ (* 71/3240 (pow (pow x 13) 1/3)) (pow x 1/3)) (* 1/18 (pow (pow x 7) 1/3)))
295.0ms
(- (+ (* 2840/729 (/ (exp (* 1/3 (- (log 3/40) (* 5 (log (/ 1 x)))))) (pow x 4))) (exp (* 1/3 (- (log 3/40) (* 5 (log (/ 1 x))))))) (* 20/27 (/ (exp (* 1/3 (- (log 3/40) (* 5 (log (/ 1 x)))))) (pow x 2))))
197.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune601.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (sqrt (+ x (hypot 1 x))))
2.6b
(log (sqrt (+ x (hypot 1 x))))
0.8b
(+ x (hypot 1 x))
0.8b
(+ x (hypot 1 x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×fma-def add-exp-log log-pow
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube sqrt-div flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
2×+-commutative sum-log sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 82
Calls
4 calls:
Slowest
4.0ms
(+ x (hypot 1 x))
4.0ms
(+ x (hypot 1 x))
4.0ms
(log (sqrt (+ x (hypot 1 x))))
4.0ms
(log (sqrt (+ x (hypot 1 x))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(log (sqrt (+ x (hypot 1 x))))
159.0ms
(log (sqrt (+ x (hypot 1 x))))
75.0ms
(+ x (hypot 1 x))
66.0ms
(+ x (hypot 1 x))

simplify2.9s

Counts
42 → 94
Calls
42 calls:
Slowest
379.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
343.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
337.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
329.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
209.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes76.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch138.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.0s2292×body1280valid
937.0ms1545×body640valid
610.0ms2214×body80valid
557.0ms788×body2560valid
240.0ms771×body320valid
74.0ms390×body160valid