Details

Time bar (total: 25.3s)

sample41.0ms

Algorithm
intervals
Results
18.0ms87×body1280valid
5.0ms136×body80valid
4.0ms20×body640valid
1.0ms8×body160valid
1.0ms5×body320valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22612
33212
43412
54012
64212
done4212

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite27.0ms

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
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def fma-neg associate-/r* sqrt-prod associate-/l*
1×cbrt-undiv +-commutative sub-neg hypot-udef flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(hypot 1.0 x)
11.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series869.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ 1.0 (hypot 1.0 x))
84.0ms
(hypot 1.0 x)
173.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
501.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts
99 → 99
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02252015
15421619
215951366
done50011249

prune314.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
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)))))))
1.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
21×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-- flip-+ div-inv associate-/l/
1×+-commutative sub-neg fma-neg diff-log div-sub prod-diff sum-log
Counts
4 → 100
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms
(/ (- (* 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 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.5s

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ 1.0 (hypot 1.0 x))
494.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.7s
(/ (- (* 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)))))))
153.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.3s

Counts
112 → 112
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03303402
19713222
238872952
done50002951

prune560.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
1.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
382×sqrt-prod
342×times-frac
332×add-sqr-sqrt
284×*-un-lft-identity
166×add-cube-cbrt
94×swap-sqr
51×distribute-lft-out
48×associate-*r* associate-*l*
25×unswap-sqr
18×add-exp-log add-cbrt-cube
12×sqrt-div
11×pow1
10×associate-/r/
8×add-log-exp
7×associate-/r*
6×associate-/l*
5×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- flip--
2×sub-neg fma-neg diff-log prod-diff associate-/l/
1×pow2 frac-times frac-2neg pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ clear-num rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 349
Calls
4 calls:
28.0ms
(/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
184.0ms
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
18.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
18.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series5.6s

Counts
4 → 12
Calls
4 calls:
3.4s
(/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.9s
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
163.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
143.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.2s

Counts
361 → 361
Iterations

Useful iterations: done (1.1s)

IterNodesCost
056727701
1181124709
done500022968

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.6b

localize42.0ms

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
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (- (* 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)))))))))
1.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
1.9b
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
86×sqrt-prod
84×times-frac
75×*-un-lft-identity
49×add-cube-cbrt
48×associate-*l*
21×associate-*r*
15×unswap-sqr
13×distribute-lft-out
11×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 associate-/r/
4×expm1-log1p-u sqrt-div associate-/r* log1p-expm1-u
3×flip3-- flip3-+ flip-- flip-+ div-inv associate-/l*
2×cbrt-undiv sub-neg sqrt-undiv fma-neg diff-log div-exp prod-diff prod-exp cbrt-unprod associate-/l/
1×frac-times frac-2neg sqrt-unprod div-sub associate-*r/ swap-sqr pow-prod-down associate-*l/ clear-num rem-square-sqrt *-commutative
Counts
4 → 175
Calls
4 calls:
28.0ms
(/ (- (* 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)))))))
172.0ms
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (- (* 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)))))))))
16.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
9.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series3.8s

Counts
4 → 12
Calls
4 calls:
1.8s
(/ (- (* 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)))))))
1.7s
(* (/ (sqrt (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (- (* 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)))))))))
187.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
170.0ms
(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.2s

Counts
187 → 187
Iterations

Useful iterations: done (2.2s)

IterNodesCost
035310940
1101310309
241459720
done50009718

prune955.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.6b

regimes370.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02058
12358
done2358

end0.0ms

sample1.3s

Algorithm
intervals
Results
745.0ms2896×body1280valid
183.0ms4020×body80valid
129.0ms621×body640valid
44.0ms292×body320valid
15.0ms171×body160valid