Details

Time bar (total: 22.0s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify33.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01114
11613
22612
33212
done3212

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
add-exp-log add-cbrt-cube add-log-exp
pow1
expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
cbrt-undiv +-commutative fma-def frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 72
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
130.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series355.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ (* x x) (* y y))
69.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
240.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.2s

Counts
81 → 81
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01341510
13071332
29331139
331261133
done50011132

prune441.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))))
0.4b
(/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))
36.9b
(sqrt (fma z z (fma x x (pow y 2))))
36.9b
(sqrt (fma z z (fma x x (pow y 2))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod
130×add-sqr-sqrt
106×times-frac
64×add-cube-cbrt *-un-lft-identity
47×cbrt-prod
43×associate-*r*
24×unswap-sqr
13×associate-*l*
10×pow1
add-exp-log
add-cbrt-cube
associate-/r* associate-/l*
expm1-log1p-u sqrt-pow1 pow1/2 sqrt-div log1p-expm1-u add-log-exp
pow-prod-down div-inv
rem-sqrt-square
cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 191
Calls
4 calls:
102.0ms
(* (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))))
16.0ms
(/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))
3.0ms
(sqrt (fma z z (fma x x (pow y 2))))
3.0ms
(sqrt (fma z z (fma x x (pow y 2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
497.0ms
(* (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))))
331.0ms
(/ (sqrt (fma z z (fma x x (pow y 2)))) (cbrt 3.0))
137.0ms
(sqrt (fma z z (fma x x (pow y 2))))
190.0ms
(sqrt (fma z z (fma x x (pow y 2))))

simplify3.6s

Counts
203 → 203
Iterations

Useful iterations: done (3.6s)

IterNodesCost
02286194
13635765
28225581
318745409
done50005387

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (pow y 2)))) (* (fabs (cbrt 3.0)) (sqrt (cbrt 3.0))))
36.9b
(sqrt (fma z z (fma x x (pow y 2))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
sqrt-prod
add-sqr-sqrt
add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
times-frac associate-/l*
pow1
cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 44
Calls
2 calls:
19.0ms
(/ (sqrt (fma z z (fma x x (pow y 2)))) (* (fabs (cbrt 3.0)) (sqrt (cbrt 3.0))))
2.0ms
(sqrt (fma z z (fma x x (pow y 2))))

series1.3s

Counts
2 → 6
Calls
2 calls:
1.2s
(/ (sqrt (fma z z (fma x x (pow y 2)))) (* (fabs (cbrt 3.0)) (sqrt (cbrt 3.0))))
160.0ms
(sqrt (fma z z (fma x x (pow y 2))))

simplify6.6s

Counts
50 → 50
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
080977
1158900
2433818
31427818
43756818
done5000818

prune266.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))))
37.0b
(sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
75×times-frac sqrt-prod
52×*-un-lft-identity
48×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
pow1
add-exp-log
associate-/r* add-cbrt-cube
sqrt-div
div-inv
expm1-log1p-u rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u associate-/l* add-log-exp
cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
3 → 148
Calls
3 calls:
10.0ms
(/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))
123.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))))
11.0ms
(sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0)))

series1.1s

Counts
3 → 9
Calls
3 calls:
147.0ms
(/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))
452.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0))))
478.0ms
(sqrt (/ (fma z z (fma x x (pow y 2))) (cbrt 3.0)))

simplify1.4s

Counts
157 → 157
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02023869
13343691
27533516
318403516
done50003488

prune750.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 7.0b

regimes249.0ms

Accuracy

37% (20.0b remaining)

Error of 26.4b against oracle of 6.4b and baseline of 38.1b

bsearch110.0ms

Steps
ItersRangePoint
8
5.669660250650512e+56
1.7629344231922744e+59
1.7466332676838354e+59
9
-1.6651412823110563e+127
-7.0065691084106e+119
-1.9079361298169978e+126

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03151
14051
24251
done4251

end0.0ms

sample684.0ms

Algorithm
intervals
Results
350.0ms8000×body80valid