Details

Time bar (total: 38.3s)

sample31.0ms

Algorithm
intervals
Results
16.0ms98×body1280valid
4.0ms123×body80valid
3.0ms21×body640valid
1.0ms10×body320valid
0.0ms4×body160valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22412
33012
43212
53812
64112
done4112

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
12×prod-diff
9×times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-prod
3×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 75
Calls
3 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series691.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(/ 1.0 (hypot 1.0 x))
255.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
338.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify521.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
02072042
14871618
215691398
done50001398

prune223.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
21×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-- flip-+ div-inv associate-/l/
1×+-commutative sub-neg fma-neg diff-log div-sub prod-diff sum-log
Counts
4 → 100
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.7s

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1.0 (hypot 1.0 x))
1.2s
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
306.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
114.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.2s

Counts
112 → 112
Iterations

Useful iterations: 2 (439.0ms)

IterNodesCost
03303402
19693222
240992952
done50012952

prune399.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.9b
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
316×times-frac
290×add-sqr-sqrt
260×*-un-lft-identity
150×add-cube-cbrt
120×difference-of-squares
117×sqr-pow
75×unpow-prod-down
56×prod-diff
44×associate-/l*
35×distribute-lft-out
20×distribute-lft-out--
14×add-exp-log add-cbrt-cube
8×cube-mult unpow3 cube-prod
7×pow1 fma-neg associate-/r* div-inv
6×add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×pow-unpow div-sub associate-/l/
2×cube-div flip3-- pow-pow frac-2neg flip3-+ associate-*l/ pow-exp clear-num associate-/r/ flip-- flip-+ rem-cube-cbrt
1×pow-to-exp sub-neg diff-log pow-prod-down prod-exp cbrt-unprod
Counts
4 → 364
Calls
4 calls:
34.0ms
(/ (/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
33.0ms
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
8.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
12.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series25.2s

Counts
4 → 12
Calls
4 calls:
22.5s
(/ (/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.1s
(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4)))
274.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
422.0ms
(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify1.2s

Counts
376 → 376
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0129736026
1388532428
done500032420

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
0.5b
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
0.9b
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
194×cbrt-prod
182×unpow-prod-down
175×prod-diff
117×add-sqr-sqrt
97×cube-prod
93×*-un-lft-identity
91×add-cube-cbrt
70×sqr-pow
28×cube-mult unpow3
21×difference-of-squares
11×add-exp-log
10×cube-div
8×pow-exp add-cbrt-cube
7×pow1 fma-neg
6×pow-unpow associate-*l/ add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-to-exp pow-pow flip3-+ flip-+ rem-cube-cbrt
2×cbrt-div prod-exp
1×sub-neg flip3-- pow1/3 diff-log pow-prod-down flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out--
Counts
4 → 319
Calls
4 calls:
8.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
4.0ms
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
4.0ms
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
28.0ms
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

series1.8s

Counts
4 → 12
Calls
4 calls:
269.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
812.0ms
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
292.0ms
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
421.0ms
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

simplify1.3s

Counts
331 → 331
Iterations

Useful iterations: 2 (475.0ms)

IterNodesCost
051622320
1117711736
241189327
done50009327

prune677.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.2b

regimes254.0ms

Accuracy

0% (0.2b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02357
12557
done2557

end0.0ms

sample823.0ms

Algorithm
intervals
Results
484.0ms2909×body1280valid
115.0ms4022×body80valid
80.0ms621×body640valid
26.0ms293×body320valid
9.0ms155×body160valid