Details

Time bar (total: 50.1s)

sample84.0ms

Algorithm
intervals
Results
50.0ms94×body1280valid
8.0ms124×body80valid
5.0ms16×body640valid
3.0ms14×body320valid
1.0ms8×body160valid

simplify49.0ms

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: 14.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
12×prod-diff
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-neg associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg hypot-udef 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
4 → 85
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(hypot 1.0 x)
26.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ 1.0 (hypot 1.0 x))
79.0ms
(hypot 1.0 x)
341.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
443.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02252149
15631727
224681491
done50001474

prune337.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.7b

localize22.0ms

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
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
2.3b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite89.0ms

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:
5.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
62.0ms
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
9.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.9s

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ 1.0 (hypot 1.0 x))
145.0ms
(/ 1.0 (hypot 1.0 x))
1.5s
(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
129.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify491.0ms

Counts
124 → 124
Iterations

Useful iterations: done (485.0ms)

IterNodesCost
02973324
19003170
done50002912

prune659.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.7b

localize24.0ms

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
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
2.3b
(- (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))

rewrite476.0ms

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
107×times-frac
100×prod-diff
68×add-sqr-sqrt
64×add-cube-cbrt
48×associate-/r/
26×div-inv
25×flip3-+ flip-+
23×distribute-lft-out
13×add-exp-log add-cbrt-cube
10×fma-neg associate-/r*
7×associate-/l*
6×add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×distribute-rgt-out-- frac-2neg clear-num
2×associate-*l/ associate-/l/ difference-of-squares
1×sub-neg flip3-- diff-log prod-exp frac-sub flip-- cbrt-unprod distribute-lft-out-- sub-div
Counts
4 → 219
Calls
4 calls:
8.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(/ 1.0 (hypot 1.0 x))
70.0ms
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
377.0ms
(- (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))

series7.0s

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ 1.0 (hypot 1.0 x))
181.0ms
(/ 1.0 (hypot 1.0 x))
2.4s
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
4.3s
(- (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))

simplify1.1s

Counts
231 → 231
Iterations

Useful iterations: done (1.0s)

IterNodesCost
047220587
1141416923
done500014070

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
0.0b
(* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
0.0b
(/ (+ 1.0 (/ 1.0 (hypot 1.0 x))) (/ (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0) 0.5))
2.3b
(- (* (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))) (* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))))

rewrite581.0ms

Algorithm
rewrite-expression-head
Rules
153×*-un-lft-identity
148×times-frac
73×add-sqr-sqrt
71×add-cube-cbrt
50×add-exp-log add-cbrt-cube
40×distribute-lft-out
20×associate-/r*
17×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×associate-*l/
12×swap-sqr
11×pow1 associate-*r/ associate-/r/ div-inv
10×associate-*r* associate-*l*
9×frac-times frac-sub
7×flip3-+ flip-+
6×add-log-exp
5×associate-/l* sub-div
4×expm1-log1p-u log1p-expm1-u associate-/l/
2×frac-2neg clear-num
1×pow2 sub-neg flip3-- pow-plus fma-neg diff-log prod-diff pow-prod-down pow-sqr *-commutative pow-prod-up flip-- difference-of-squares unswap-sqr
Counts
4 → 232
Calls
4 calls:
64.0ms
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
285.0ms
(* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
107.0ms
(/ (+ 1.0 (/ 1.0 (hypot 1.0 x))) (/ (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0) 0.5))
109.0ms
(- (* (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))) (* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))))

series27.0s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
6.6s
(* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
1.9s
(/ (+ 1.0 (/ 1.0 (hypot 1.0 x))) (/ (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0) 0.5))
16.5s
(- (* (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* 1.0 1.0) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))) (* (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)) (/ (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))))

simplify2.0s

Counts
244 → 244
Iterations

Useful iterations: done (2.0s)

IterNodesCost
080017512
1286115704
done500114482

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.6b

regimes218.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
022121
126121
done26121

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.5s2926×body1280valid
383.0ms3978×body80valid
187.0ms602×body640valid
117.0ms321×body320valid
20.0ms173×body160valid