Details

Time bar (total: 12.6s)

sample55.0ms

Algorithm
intervals
Results
27.0ms87×body1280valid
7.0ms130×body80valid
5.0ms20×body640valid
2.0ms13×body320valid
1.0ms6×body160valid

simplify57.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* 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 sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
0.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
17.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series243.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(hypot 1.0 x)
14.0ms
(/ 1.0 (hypot 1.0 x))
102.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
123.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.1s

Counts
73 → 73

prune225.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b
(+ (* 1.0 1.0) (- (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
7×pow1
6×associate-/r* associate-/l*
5×sqrt-div
3×flip3-+ flip-+
2×cbrt-undiv frac-times associate-+r+ distribute-neg-in frac-2neg sqrt-pow1 associate-*r/ div-exp clear-num sum-log div-inv
1×+-commutative neg-sub0 distribute-rgt-in associate-+r- distribute-lft-in pow1/2 unsub-neg pow-prod-down neg-log associate-*l/ sqrt-prod
Counts
4 → 87
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
23.0ms
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms
(+ (* 1.0 1.0) (- (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series135.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
34.0ms
(+ (* 1.0 1.0) (- (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify612.0ms

Counts
99 → 99

prune475.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
2.1b
(+ (* 1.0 (- 1.0 (/ 1.0 2.0))) (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
10×associate-*r/
8×add-exp-log add-cbrt-cube add-log-exp
7×pow1
6×frac-add associate-/r* distribute-neg-frac associate-/l*
5×sqrt-div
4×frac-times associate-+l+
3×flip3-- flip3-+ associate-*l/ flip-- flip-+
2×cbrt-undiv distribute-rgt-in sub-neg frac-2neg distribute-lft-in sqrt-pow1 div-exp clear-num sum-log div-inv
1×+-commutative neg-sub0 associate-+r- pow1/2 unsub-neg pow-prod-down neg-log sqrt-prod
Counts
4 → 95
Calls
4 calls:
29.0ms
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms
(/ 1.0 (hypot 1.0 x))
17.0ms
(/ 1.0 (hypot 1.0 x))
20.0ms
(+ (* 1.0 (- 1.0 (/ 1.0 2.0))) (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))))

series166.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
44.0ms
(+ (* 1.0 (- 1.0 (/ 1.0 2.0))) (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))))

simplify742.0ms

Counts
107 → 107

prune452.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (- (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (* 1.0 (- 1.0 (/ 1.0 2.0))))) (* (* 1.0 (- 1.0 (/ 1.0 2.0))) (* 1.0 (- 1.0 (/ 1.0 2.0))))))
0.1b
(pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)
2.1b
(- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
899×associate-*r/
473×frac-times
408×distribute-neg-frac
346×flip3-- flip--
282×associate-/r/
280×frac-add
235×associate-*l/
204×frac-sub
47×add-sqr-sqrt
37×*-un-lft-identity
36×times-frac
27×cube-div add-cube-cbrt
21×add-exp-log add-cbrt-cube sqr-pow
20×difference-of-squares
12×associate-/l*
8×associate-/l/
7×pow1
6×cbrt-undiv div-exp associate-/r* add-log-exp
5×difference-cubes pow-exp distribute-lft-out-- rem-cube-cbrt
4×prod-exp cbrt-unprod
3×pow-unpow
2×pow-pow frac-2neg clear-num div-inv
1×cube-mult pow-to-exp sub-neg unpow-prod-down flip3-+ diff-log unpow3 div-sub cube-prod pow-prod-down flip-+
Counts
4 → 424
Calls
4 calls:
12.0ms
(/ 1.0 (hypot 1.0 x))
141.0ms
(/ (- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (- (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (* 1.0 (- 1.0 (/ 1.0 2.0))))) (* (* 1.0 (- 1.0 (/ 1.0 2.0))) (* 1.0 (- 1.0 (/ 1.0 2.0))))))
30.0ms
(pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)
33.0ms
(- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3))

series455.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1.0 (hypot 1.0 x))
291.0ms
(/ (- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (- (- (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x)))) (* 1.0 (- 1.0 (/ 1.0 2.0))))) (* (* 1.0 (- 1.0 (/ 1.0 2.0))) (* 1.0 (- 1.0 (/ 1.0 2.0))))))
46.0ms
(pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3)
105.0ms
(- (pow (* 1.0 (- 1.0 (/ 1.0 2.0))) 3) (pow (* (/ 1.0 2.0) (/ 1.0 (hypot 1.0 x))) 3))

simplify1.3s

Counts
436 → 436

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

regimes231.0ms

Accuracy

0% (0.3b remaining)

Error of 15.4b against oracle of 15.1b and baseline of 15.4b

bsearch0.0ms

simplify305.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s2825×body1280valid
208.0ms665×body640valid
194.0ms4040×body80valid
45.0ms309×body320valid
15.0ms161×body160valid