Details

Time bar (total: 1.4m)

sample136.0ms

Algorithm
intervals
Results
72.0ms77×body1280valid
26.0ms52×body640valid
15.0ms22×body2560valid
7.0ms24×body320valid
5.0ms74×body80valid
1.0ms7×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b
(log (+ x (hypot 1 x)))
0.6b
(+ x (hypot 1 x))

rewrite8.0ms

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
4.0ms
(+ x (hypot 1 x))
3.0ms
(log (+ x (hypot 1 x)))

series598.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
536.0ms
(log (+ x (hypot 1 x)))
62.0ms
(+ x (hypot 1 x))

simplify1.6s

Counts
17 → 42
Calls
17 calls:
Slowest
337.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
293.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
241.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
183.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
152.0ms
(log (+ (pow x 3) (pow (hypot 1 x) 3)))

prune370.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

14.9b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.4b
(* 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 3/40 (pow x 5) x)
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

series247.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
154.0ms
(fma 3/40 (pow x 5) x)
74.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
19.0ms
(* x -1/6)

simplify955.0ms

Counts
18 → 52
Calls
18 calls:
Slowest
157.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
156.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
131.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
119.0ms
(+ x (* 3/40 (pow x 5)))
118.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))

prune517.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

17.8b
(+ (+ (/ 1/4 (* x x)) (log 2)) (/ -3/32 (* (* x x) (* x x))))
0.2b
(/ 1/4 (* x x))
0.2b
(/ -3/32 (* (* x x) (* x x)))
0.1b
(* (* x x) (* x x))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
19×*-un-lft-identity
18×pow-plus
17×prod-exp cbrt-unprod
13×pow2
9×add-sqr-sqrt add-cube-cbrt
8×add-log-exp
7×cbrt-undiv div-exp distribute-lft-out
6×times-frac associate-/l*
5×fma-def
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×sum-log
2×clear-num associate-/r* frac-2neg flip3-+ frac-add log-pow flip-+ div-inv
1×+-commutative associate-+l+ swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
4 → 146
Calls
4 calls:
Slowest
149.0ms
(+ (+ (/ 1/4 (* x x)) (log 2)) (/ -3/32 (* (* x x) (* x x))))
40.0ms
(/ -3/32 (* (* x x) (* x x)))
30.0ms
(* (* x x) (* x x))
7.0ms
(/ 1/4 (* x x))

series217.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(+ (+ (/ 1/4 (* x x)) (log 2)) (/ -3/32 (* (* x x) (* x x))))
51.0ms
(/ -3/32 (* (* x x) (* x x)))
36.0ms
(* (* x x) (* x x))
32.0ms
(/ 1/4 (* x x))

simplify7.6s

Counts
122 → 158
Calls
122 calls:
Slowest
577.0ms
(+ (* (- (* (/ 1/4 (* x x)) (/ 1/4 (* x x))) (* (log 2) (log 2))) (* (* x x) (* x x))) (* (- (/ 1/4 (* x x)) (log 2)) -3/32))
484.0ms
(* (+ (* (/ 1/4 (* x x)) (/ 1/4 (* x x))) (- (* (log 2) (log 2)) (* (/ 1/4 (* x x)) (log 2)))) (* (* x x) (* x x)))
390.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
363.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
353.0ms
(/ (* (* 1/4 1/4) 1/4) (* (* (* x x) x) (* (* x x) x)))

prune1.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

22.0b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
10.7b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.1b
(/ (/ 1/8 x) (* x x))
0.1b
(/ 1/16 (pow x 5))

rewrite217.0ms

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
104.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
90.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
13.0ms
(/ (/ 1/8 x) (* x x))
5.0ms
(/ 1/16 (pow x 5))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
93.0ms
(/ 1/16 (pow x 5))
59.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
46.0ms
(/ (/ 1/8 x) (* x x))

simplify1.1m

Counts
329 → 261
Calls
329 calls:
Slowest
726.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
689.0ms
(fma (- (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) 1 (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) 1))
651.0ms
(fma (- (+ (/ 1/16 (pow x 5)) (/ 1/2 x))) 1 (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) 1))
447.0ms
(log (sqrt (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))))
435.0ms
(fma (/ (/ (* (cbrt 1/8) (cbrt 1/8)) 1) x) (/ (/ (cbrt 1/8) x) x) (- (* (+ (/ 1/16 (pow x 5)) (/ 1/2 x)) (/ 1 1))))

prune2.4s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch130.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.4s2374×body1280valid
874.0ms1535×body640valid
595.0ms808×body2560valid
254.0ms2125×body80valid
240.0ms749×body320valid
137.0ms409×body160valid