Details

Time bar (total: 13.2s)

sample58.0ms

Algorithm
intervals
Results
26.0ms80×body1280valid
8.0ms138×body80valid
6.0ms23×body640valid
2.0ms12×body320valid
0.0ms3×body160valid

simplify54.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.1b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series156.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(/ 1.0 (hypot 1.0 x))
144.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify643.0ms

Counts
47 → 47

prune122.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 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))))))
0.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt times-frac
8×add-exp-log associate-*r/ add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/
3×sub-neg
2×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×+-commutative diff-log div-sub sum-log
Counts
4 → 95
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
47.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
18.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
210.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
117.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
39.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify729.0ms

Counts
107 → 107

prune356.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.5b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite535.0ms

Algorithm
rewrite-expression-head
Rules
80×associate-*r/
50×sqrt-div
26×flip3-+ flip-+
18×frac-sub
13×add-log-exp
8×pow1 frac-times
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*l/
5×add-exp-log sub-neg add-cbrt-cube
4×unpow-prod-down pow-pow cube-prod associate--l+ sub-div
3×pow-unpow flip3-- diff-log flip--
2×cube-div distribute-rgt-in associate-+r+ distribute-lft-in sqrt-pow1 sum-log sqrt-prod
1×+-commutative cube-mult pow-to-exp associate-+r- distribute-rgt-out-- pow1/2 unpow3 pow-prod-down pow-exp sqrt-pow2 rem-cube-cbrt sqr-pow
Counts
4 → 97
Calls
4 calls:
342.0ms
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
29.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
19.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
135.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series929.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
161.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
46.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
392.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify1.6s

Counts
109 → 109

prune606.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
0.0b
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
0.6b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
288×associate-*r/
108×frac-add
76×flip3-- flip--
74×associate-/r/
72×frac-times
40×add-sqr-sqrt
30×*-un-lft-identity
27×times-frac associate-*l/
21×add-exp-log add-cbrt-cube sqr-pow
20×add-cube-cbrt difference-of-squares
19×flip3-+ flip-+
12×pow1
9×cube-div associate-/l*
7×prod-exp cbrt-unprod
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×pow-prod-down frac-sub associate-/l/
3×cbrt-undiv pow-unpow div-exp associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×pow-pow
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in diff-log unpow3 div-sub cube-prod associate-*l* clear-num *-commutative div-inv
Counts
4 → 206
Calls
4 calls:
74.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
209.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
25.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
42.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series483.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
256.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
41.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
84.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify1.1s

Counts
218 → 218

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.2b

regimes230.0ms

Accuracy

0.1% (0.3b remaining)

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

bsearch0.0ms

simplify547.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s2896×body1280valid
692.0ms588×body640valid
243.0ms4043×body80valid
119.0ms326×body320valid
18.0ms147×body160valid