Details

Time bar (total: 56.1s)

sample54.0ms

Algorithm
intervals
Results
26.0ms93×body1280valid
7.0ms129×body80valid
4.0ms18×body640valid
2.0ms11×body320valid
1.0ms5×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22612
33212
43412
54012
64312
done4312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
1.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
12×prod-diff
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u fma-neg associate-/r* sqrt-prod log1p-expm1-u associate-/l*
1×cbrt-undiv sub-neg hypot-udef flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 70
Calls
3 calls:
0.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series680.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(hypot 1.0 x)
132.0ms
(/ 1.0 (hypot 1.0 x))
484.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts
79 → 79
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02021787
14891414
221131174
done50011157

prune405.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.6b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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:
59.0ms
(/ (- (* 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))
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
15.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.0s

Counts
4 → 12
Calls
4 calls:
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))
139.0ms
(/ 1.0 (hypot 1.0 x))
155.0ms
(/ 1.0 (hypot 1.0 x))
143.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.4s

Counts
124 → 124
Iterations

Useful iterations: 2 (901.0ms)

IterNodesCost
02973324
19003170
249652910
done50002910

prune649.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.6b

localize44.0ms

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) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
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) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
1.1b
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
64×prod-diff
46×add-sqr-sqrt
36×sqr-pow
34×*-un-lft-identity
26×add-cube-cbrt
24×unpow-prod-down cube-prod difference-of-squares
18×cube-mult unpow3
14×add-exp-log add-cbrt-cube
13×times-frac associate-/l*
9×pow1
8×fma-neg
6×add-log-exp
4×expm1-log1p-u associate-*r/ associate-*r* log1p-expm1-u
3×difference-cubes pow-unpow flip3-+ associate-*l* prod-exp cbrt-unprod flip-+ distribute-lft-out--
2×cbrt-undiv cube-div flip3-- pow-pow div-exp pow-prod-down associate-*l/ pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×distribute-rgt-in pow-to-exp sub-neg frac-2neg distribute-lft-in diff-log div-sub clear-num associate-/r* *-commutative div-inv distribute-lft-out unswap-sqr
Counts
4 → 195
Calls
4 calls:
17.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
70.0ms
(* (fma 1.0 (pow 1.0 3) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
74.0ms
(/ (- (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) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
20.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series37.7s

Counts
4 → 12
Calls
4 calls:
447.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.6s
(* (fma 1.0 (pow 1.0 3) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
35.2s
(/ (- (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) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)))
494.0ms
(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify2.5s

Counts
207 → 207
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0106518872
1353715701
done500114663

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.8b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×log-prod associate-/r* associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log-pow log1p-expm1-u
3×exp-prod exp-sum
2×cbrt-undiv sub-neg frac-2neg div-exp prod-diff clear-num div-inv
1×log-div flip3-- exp-diff fma-neg diff-log rem-log-exp flip--
Counts
4 → 95
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
27.0ms
(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

series676.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ 1.0 (hypot 1.0 x))
178.0ms
(/ 1.0 (hypot 1.0 x))
189.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
165.0ms
(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

simplify1.4s

Counts
107 → 107
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01581605
13801513
218261346
done50021324

prune762.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.8b

regimes441.0ms

Accuracy

85.4% (0.3b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 14.8b

bsearch2.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
063187
170187
done70187

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.1s2847×body1280valid
740.0ms4053×body80valid
196.0ms641×body640valid
55.0ms313×body320valid
16.0ms146×body160valid