Details

Time bar (total: 3.7s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0136
1206
2226
3226

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
3.0ms
(+ (* x x) (* y y))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series126.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(+ (* x x) (* y y))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify63.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0173212
1707203
21993203
35001202

prune89.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
0.2b
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
35.5b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×cbrt-div
7×pow1
6×add-exp-log add-cbrt-cube
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1 associate-*r/
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 74
Calls
4 calls:
14.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
52.0ms
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
8.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
7.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
140.0ms
(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
102.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))
103.0ms
(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify52.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03201178
113041101
250011084

prune293.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
6.0b
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×add-exp-log flip3-+ log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square sum-log rem-exp-log
Counts
3 → 48
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
10.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* x x) (* y y))
98.0ms
(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify67.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0220425
1776411
22094396
35001388

prune134.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.9b

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×pow-unpow sqrt-prod
6×cbrt-prod sqrt-div
5×add-log-exp
4×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube
3×unpow-prod-down rem-sqrt-square pow-pow flip3-+ log-pow flip-+
1×pow-to-exp exp-prod exp-to-pow pow-exp sqr-pow
Counts
4 → 70
Calls
4 calls:
3.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
01901221
15591124
219881118
350011114

prune289.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.9b

regimes432.0ms

Accuracy

63.6% (7.0b remaining)

Error of 25.7b against oracle of 18.7b and baseline of 38.0b

bsearch59.0ms

Steps
ItersRangePoint
7
2.8540072411378333e+150
6.799686113877851e+152
7.792733426685086e+150
10
-2.036247561034917e+138
-1.3682670211914512e+128
-1.895586491161729e+137

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample408.0ms

Algorithm
intervals
Results
243.0ms8000×body80valid