Details

Time bar (total: 19.4s)

sample92.0ms

Algorithm
intervals
Results
42.0ms71×body1280valid
21.0ms57×body640valid
9.0ms21×body2560valid
7.0ms34×body320valid
4.0ms65×body80valid
1.0ms8×body160valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize18.0ms

Local error

Found 3 expressions with local error:

2.6b
(log (+ x (hypot 1 x)))
0.4b
(+ x (hypot 1 x))
0.0b
(hypot 1 x)

rewrite11.0ms

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
(log (+ x (hypot 1 x)))
4.0ms
(+ x (hypot 1 x))
0.0ms
(hypot 1 x)

series316.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
169.0ms
(log (+ x (hypot 1 x)))
101.0ms
(+ x (hypot 1 x))
46.0ms
(hypot 1 x)

simplify2.4s

Counts
20 → 56
Calls
20 calls:
Slowest
344.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
343.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
263.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
262.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
228.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune575.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

13.5b
(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)

rewrite7.0ms

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
6.0ms
(* 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)

series278.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
172.0ms
(fma 3/40 (pow x 5) x)
81.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
25.0ms
(* x -1/6)

simplify1.2s

Counts
18 → 52
Calls
18 calls:
Slowest
207.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
185.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))
182.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
173.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
135.0ms
(+ x (* 3/40 (pow x 5)))

prune488.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (sqrt (+ x (hypot 1 x))))
2.6b
(log (sqrt (+ x (hypot 1 x))))
0.4b
(+ x (hypot 1 x))
0.4b
(+ 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))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(log (sqrt (+ x (hypot 1 x))))
167.0ms
(log (sqrt (+ x (hypot 1 x))))
91.0ms
(+ x (hypot 1 x))
79.0ms
(+ x (hypot 1 x))

simplify3.1s

Counts
42 → 94
Calls
42 calls:
Slowest
414.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
364.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
360.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
323.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
257.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune792.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (sqrt (+ x (hypot 1 x))))
2.6b
(log (+ x (hypot 1 x)))
0.4b
(+ x (hypot 1 x))
0.4b
(+ x (hypot 1 x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
11×log-prod
9×add-sqr-sqrt add-cube-cbrt
8×add-log-exp
7×pow1
6×fma-def add-exp-log
4×expm1-log1p-u log-div flip3-+ add-cbrt-cube log-pow sqrt-prod flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
2×+-commutative sum-log sqrt-div rem-log-exp
1×sqrt-pow1 pow1/2
Counts
4 → 77
Calls
4 calls:
Slowest
4.0ms
(+ x (hypot 1 x))
4.0ms
(+ x (hypot 1 x))
4.0ms
(log (sqrt (+ x (hypot 1 x))))
3.0ms
(log (+ x (hypot 1 x)))

series505.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(log (+ x (hypot 1 x)))
149.0ms
(log (sqrt (+ x (hypot 1 x))))
82.0ms
(+ x (hypot 1 x))
75.0ms
(+ x (hypot 1 x))

simplify3.4s

Counts
38 → 89
Calls
38 calls:
Slowest
379.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
373.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
345.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
339.0ms
(log (sqrt (+ (pow x 3) (pow (hypot 1 x) 3))))
250.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))

prune742.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.0b

bsearch146.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.1s2364×body1280valid
1.2s1562×body640valid
535.0ms758×body2560valid
295.0ms805×body320valid
263.0ms2126×body80valid
105.0ms385×body160valid