Details

Time bar (total: 1.2m)

sample147.0ms

Algorithm
intervals
Results
80.0ms82×body1280valid
24.0ms52×body640valid
18.0ms30×body2560valid
6.0ms20×body320valid
5.0ms60×body80valid
2.0ms12×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.4b

localize17.0ms

Local error

Found 2 expressions with local error:

3.1b
(log (+ x (hypot 1 x)))
0.6b
(+ x (hypot 1 x))

rewrite16.0ms

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)))

series283.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
177.0ms
(log (+ x (hypot 1 x)))
105.0ms
(+ x (hypot 1 x))

simplify2.0s

Counts
17 → 42
Calls
17 calls:
Slowest
353.0ms
(log (sqrt (+ x (hypot 1 x))))
319.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
266.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
255.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
204.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))

prune377.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

15.4b
(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
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)

series290.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
182.0ms
(fma 3/40 (pow x 5) x)
86.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
22.0ms
(* x -1/6)

simplify1.1s

Counts
18 → 52
Calls
18 calls:
Slowest
186.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
182.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
159.0ms
(+ x (* 3/40 (pow x 5)))
155.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
150.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))

prune542.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

22.3b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
12.9b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.1b
(/ (/ 1/8 x) (* x x))
0.0b
(/ 1/16 (pow x 5))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
224×times-frac
212×*-un-lft-identity
114×add-sqr-sqrt
100×add-cube-cbrt
85×prod-diff
36×distribute-lft-out
22×add-exp-log
18×add-cbrt-cube
17×fma-neg
16×div-inv associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- sqr-pow
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add prod-exp cbrt-unprod flip-+ flip--
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+ associate-/l/
Counts
4 → 249
Calls
4 calls:
Slowest
105.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
79.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
20.0ms
(/ (/ 1/8 x) (* x x))
10.0ms
(/ 1/16 (pow x 5))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
71.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
55.0ms
(/ 1/16 (pow x 5))
45.0ms
(/ (/ 1/8 x) (* x x))

simplify1.0m

Counts
329 → 261
Calls
329 calls:
Slowest
715.0ms
(fma (- (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) 1 (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) 1))
679.0ms
(/ (exp (/ (/ 1/8 x) (* x x))) (* (exp (/ 1/16 (pow x 5))) (exp (/ 1/2 x))))
418.0ms
(fma (* (cbrt (/ (/ 1/8 x) (* x x))) (cbrt (/ (/ 1/8 x) (* x x)))) (cbrt (/ (/ 1/8 x) (* x x))) (- (* (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (sqrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))))
417.0ms
(fma (/ (/ (sqrt 1/8) (sqrt x)) x) (/ (/ (sqrt 1/8) (sqrt x)) x) (- (* (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (* (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) (cbrt (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))))))
410.0ms
(fma (/ (/ (* (cbrt 1/8) (cbrt 1/8)) 1) x) (/ (/ (cbrt 1/8) x) x) (- (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) (/ 1 1))))

prune2.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.7b

bsearch131.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.6s2381×body1280valid
889.0ms1586×body640valid
668.0ms796×body2560valid
297.0ms810×body320valid
211.0ms2048×body80valid
82.0ms379×body160valid