Details

Time bar (total: 43.8s)

sample66.0ms

Algorithm
intervals
Results
32.0ms88×body1280valid
9.0ms135×body80valid
5.0ms16×body640valid
3.0ms15×body320valid
0.0ms2×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22612
33212
43412
54012
64312
done4312

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def fma-neg associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
23.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
27.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms
(/ 1.0 (hypot 1.0 x))
16.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
189.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
349.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
137.0ms
(/ 1.0 (hypot 1.0 x))
542.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.1s

Counts
104 → 104
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02232270
15641839
224901595
done50011579

prune382.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.6b

localize29.0ms

Local error

Found 4 expressions with local error:

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 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg flip3-+ fma-neg diff-log div-sub prod-diff flip-+
Counts
4 → 112
Calls
4 calls:
55.0ms
(/ (- (* 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)))))))
9.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(/ 1.0 (hypot 1.0 x))
17.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (- (* 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)))))))
146.0ms
(/ 1.0 (hypot 1.0 x))
153.0ms
(/ 1.0 (hypot 1.0 x))
139.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify516.0ms

Counts
124 → 124
Iterations

Useful iterations: done (511.0ms)

IterNodesCost
02973324
18993170
done50002912

prune610.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.6b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
102×times-frac
100×prod-diff
62×add-sqr-sqrt
58×add-cube-cbrt
50×associate-/r/
26×flip3-+ flip-+ div-inv
25×distribute-lft-out
16×add-exp-log add-cbrt-cube
11×associate-/r*
10×fma-neg
6×add-log-exp
5×cbrt-undiv div-exp associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×distribute-rgt-out-- frac-2neg clear-num
2×associate-*l/ prod-exp cbrt-unprod associate-/l/ difference-of-squares
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 217
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
39.0ms
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
134.0ms
(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series8.0s

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1.0 (hypot 1.0 x))
1.2s
(/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0s
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
4.7s
(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify1.2s

Counts
229 → 229
Iterations

Useful iterations: done (1.2s)

IterNodesCost
050921206
1156617507
done500014634

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.6b

localize92.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.9b
(- (/ (* 1.0 1.0) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
1.7b
(- (* (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)))))))

rewrite786.0ms

Algorithm
rewrite-expression-head
Rules
384×*-un-lft-identity
280×times-frac
226×prod-diff
155×distribute-lft-out
132×unpow-prod-down cube-prod
78×associate-*r/
76×add-sqr-sqrt
72×add-cube-cbrt
66×associate-/r/
59×flip3-+ flip-+
52×sqrt-div
33×div-inv
31×sum-cubes
17×frac-sub
16×fma-neg
12×pow1
8×frac-times pow-pow add-log-exp
6×add-exp-log pow-unpow associate-*l/ add-cbrt-cube
5×sub-div
4×cube-div expm1-log1p-u distribute-rgt-out-- sqrt-pow1 sqrt-prod log1p-expm1-u
2×cube-mult pow-to-exp sub-neg flip3-- pow1/2 diff-log unpow3 pow-prod-down pow-exp sqrt-pow2 flip-- rem-cube-cbrt difference-of-squares sqr-pow
1×distribute-lft-out--
Counts
4 → 365
Calls
4 calls:
16.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
25.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
521.0ms
(- (/ (* 1.0 1.0) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
166.0ms
(- (* (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)))))))

series18.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.0s
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
15.3s
(- (/ (* 1.0 1.0) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
1.2s
(- (* (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
377 → 377
Iterations

Useful iterations: done (1.5s)

IterNodesCost
072248314
1228939135
done500137973

prune2.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.6b

regimes266.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01326
11526
done1526

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s2874×body1280valid
723.0ms4004×body80valid
150.0ms627×body640valid
57.0ms336×body320valid
18.0ms159×body160valid