Details

Time bar (total: 46.4s)

sample87.0ms

Algorithm
intervals
Results
51.0ms98×body1280valid
9.0ms123×body80valid
5.0ms18×body640valid
3.0ms12×body320valid
1.0ms5×body160valid

simplify25.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
12212
23512
34312
done4312

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:
1.0ms
(hypot 1.0 x)
34.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
112.0ms
(hypot 1.0 x)
487.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
126.0ms
(/ 1.0 (hypot 1.0 x))
519.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify4.0s

Counts
97 → 97
Iterations

Useful iterations: done (4.0s)

IterNodesCost
02252149
128481581
done50001554

prune458.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 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))
1.8b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 91
Calls
4 calls:
7.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(/ 1.0 (hypot 1.0 x))
18.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series1.1s

Counts
4 → 12
Calls
4 calls:
528.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
185.0ms
(/ 1.0 (hypot 1.0 x))
145.0ms
(/ 1.0 (hypot 1.0 x))
212.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.3s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01901534
116641428
done50011312

prune580.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
0.0b
(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.7b
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
64×prod-diff
51×*-un-lft-identity
48×sqr-pow
41×add-cube-cbrt
40×difference-of-squares
39×times-frac
28×unpow-prod-down cube-prod
18×cube-mult unpow3
14×add-exp-log add-cbrt-cube
13×associate-/l*
12×pow1
8×fma-neg
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×expm1-log1p-u pow-prod-down associate-*l/ prod-exp cbrt-unprod log1p-expm1-u
3×pow-unpow associate-*l* associate-/r*
2×cube-div flip3-- pow-pow flip3-+ associate-*r/ pow-exp flip-- flip-+ associate-/l/ rem-cube-cbrt
1×cbrt-undiv pow-to-exp sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv
Counts
4 → 216
Calls
4 calls:
81.0ms
(* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
79.0ms
(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
31.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
23.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series4.8s

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
2.9s
(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
824.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
587.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify3.7s

Counts
228 → 228
Iterations

Useful iterations: done (3.6s)

IterNodesCost
051913834
done500110286

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b
(* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
0.0b
(/ (- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.7b
(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity
9×pow1 add-cube-cbrt
8×pow-prod-down
6×add-log-exp
5×times-frac associate-*r* associate-/l*
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×difference-cubes pow-unpow flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ difference-of-squares
2×cbrt-undiv cube-div flip3-- pow-pow div-exp associate-*l/ pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in fma-neg diff-log unpow3 div-sub cube-prod prod-diff clear-num associate-/r* sum-cubes *-commutative div-inv distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 102
Calls
4 calls:
29.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
63.0ms
(* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
123.0ms
(/ (- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
26.0ms
(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

series20.8s

Counts
4 → 12
Calls
4 calls:
452.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.4s
(* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))
17.2s
(/ (- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))) (* (fma 1.0 (pow 1.0 3) (* (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (+ (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))
1.8s
(- (* (pow (* 1.0 1.0) 3) (pow (* 1.0 1.0) 3)) (* (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))

simplify645.0ms

Counts
114 → 114
Iterations

Useful iterations: done (636.0ms)

IterNodesCost
064811104
done50009069

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

regimes502.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch233.0ms

Steps
ItersRangePoint
10
1.0194597579740466e-06
20796729.49276672
0.0006663327301348303
8
-9.640722949014248e-05
-1.9918553488737634e-08
-9.494777107334508e-05

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
055229
161229
done61229

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s2834×body1280valid
310.0ms4075×body80valid
189.0ms609×body640valid
55.0ms327×body320valid
17.0ms155×body160valid