Details

Time bar (total: 8.4s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
01114
11613
22612
33012
done3012

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.6b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×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:
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series262.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* x x) (* y y))
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
179.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.9s

Counts
81 → 81
Iterations

Useful iterations: 3 (570.0ms)

IterNodesCost
01341510
13091332
210661139
346311133
done50001133

prune281.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma x x (* y y))
0.4b
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.5b
(sqrt (fma z z (fma x x (* y y))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×sqrt-prod
16×*-un-lft-identity associate-*r*
14×add-cube-cbrt
13×times-frac
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u sqrt-pow1 pow1/2 pow-prod-down log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-unprod sqrt-div associate-*r/ prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 72
Calls
3 calls:
0.0ms
(fma x x (* y y))
16.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
1.0ms
(sqrt (fma z z (fma x x (* y y))))

series355.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma x x (* y y))
192.0ms
(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
122.0ms
(sqrt (fma z z (fma x x (* y y))))

simplify1.0s

Counts
81 → 81
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
01121300
11901182
24541115
316211115
done50001115

prune232.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.5b
(sqrt (fma z z (fma x x (* y y))))
35.5b
(sqrt (fma z z (fma x x (* y y))))
35.6b
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2 sqrt-div
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 114
Calls
4 calls:
4.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
1.0ms
(sqrt (fma z z (fma x x (* y y))))
14.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
259.0ms
(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
120.0ms
(sqrt (fma z z (fma x x (* y y))))
120.0ms
(sqrt (fma z z (fma x x (* y y))))
253.0ms
(sqrt (* (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0)) (/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))))

simplify886.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
01252466
11822013
23601939
314321939
done50011939

prune381.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp
Counts
1 → 24
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(* x (sqrt 0.3333333333333333))

simplify1.1s

Counts
27 → 27
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
039168
171151
2184143
3335143
4495143
51103143
done5000143

prune46.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.9b

regimes294.0ms

Accuracy

37% (20.0b remaining)

Error of 26.5b against oracle of 6.5b and baseline of 38.3b

bsearch141.0ms

Steps
ItersRangePoint
8
1.5491720421655856e+95
6.147715137559524e+97
4.244899767656578e+97
8
1.7074207915129012e-270
4.835147110927186e-268
1.722563062099152e-270
9
-1.7476729797984468e-228
-7.365325760942331e-238
-9.045780566004202e-238
6
-3.1442305190809916e+143
-5.062787100137526e+142
-7.514594408204408e+142

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03364
14364
25064
done5064

end0.0ms

sample448.0ms

Algorithm
intervals
Results
274.0ms8000×body80valid