Details

Time bar (total: 4.5s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite143.0ms

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×associate-/r* associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 65
Calls
3 calls:
14.0ms
(+ (* x x) (* y y))
92.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series249.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* x x) (* y y))
44.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
177.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify116.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0294707
11224644
24405642
35001640

prune198.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite125.0ms

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
9×sqrt-div
8×pow1 unswap-sqr
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-times associate-*l/
1×+-commutative rem-sqrt-square sqrt-unprod associate-*r/ prod-exp sum-log *-commutative cbrt-unprod div-inv
Counts
3 → 75
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
85.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series271.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* x x) (* y y))
156.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
91.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify124.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0318858
11226828
24730804
35002796

prune206.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 sqrt-div
3×flip3-+ flip-+
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 89
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
51.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series316.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* x x) (* y y))
202.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
90.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify94.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
02941188
110831124
240831101
350011101

prune228.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.9b
(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod
72×times-frac
60×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
40×log-prod exp-sum
6×pow1 add-exp-log associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×exp-prod sqrt-div
3×flip3-+ flip-+
2×div-inv associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square log-div sqrt-undiv frac-2neg sqrt-pow1 pow1/2 exp-diff div-exp clear-num sum-log log-pow rem-exp-log
Counts
4 → 142
Calls
4 calls:
8.0ms
(+ (* x x) (* y y))
51.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
24.0ms
(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* x x) (* y y))
205.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
205.0ms
(exp (log (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))
92.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify53.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04612082
115491970
250011901

prune360.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.1b

regimes593.0ms

Accuracy

47.7% (13.8b remaining)

Error of 26.5b against oracle of 12.7b and baseline of 39.0b

bsearch119.0ms

Steps
ItersRangePoint
9
6.028173829002919e+122
5.945452091760561e+127
3.353544466640978e+127
8
2.9004987402572773e-24
2.15302222000921e-20
1.4355555314202644e-23
7
9.422185270864312e-64
5.568387801196678e-62
5.47903429916612e-62
7
-5.922742849582995e+94
-2.6088563076195276e+93
-5.863764366255271e+94

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14628
24628

end0.0ms

sample484.0ms

Algorithm
intervals
Results
253.0ms8000×body80valid