Details

Time bar (total: 2.6s)

analyze15.0ms (0.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
49.9%49.9%0.1%5
74.9%25%0.1%6
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14

sample21.0ms (0.8%)

Algorithm
1×intervals
Results
12.0ms256×body80valid

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02114
12114

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 35.7b

Counts
2 → 1

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.1b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls

3 calls:

9.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
7.0ms
(+ (+ (* x x) (* y y)) (* z z))

series49.0ms (1.9%)

Counts
3 → 9
Calls

3 calls:

27.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))
13.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
10.0ms
(+ (+ (* x x) (* y y)) (* z z))

simplify43.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050051330

prune323.0ms (12.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New71576
Fresh000
Picked101
Done000
Total72577

Merged error: 17.3b

Counts
77 → 5

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.3b
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
33.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite33.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
34×add-sqr-sqrt
29×sqrt-prod
17×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
13×times-frac
11×add-log-exp
9×pow1 sqrt-div
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sum-log
3×sqrt-pow1 pow1/2 pow-prod-down
2×+-commutative frac-times associate-*l/
1×rem-sqrt-square associate-+r+ sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 88
Calls

4 calls:

14.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
7.0ms
(+ (* x x) (+ (* y y) (* z z)))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
4.0ms
(+ (* y y) (* z z))

series64.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

27.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
21.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
5.0ms
(+ (* y y) (* z z))

simplify50.0ms (1.9%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049991672
149991672

prune165.0ms (6.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh044
Picked011
Done000
Total1005105

Merged error: 17.3b

Counts
105 → 5

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.0b
(+ (* y y) (* z z))
0.4b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
33.1b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite28.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+r+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 102
Calls

4 calls:

9.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
4.0ms
(+ (* y y) (* z z))

series66.0ms (2.6%)

Counts
4 → 12
Calls

4 calls:

30.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
21.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
5.0ms
(+ (* y y) (* z z))

simplify52.0ms (2%)

Algorithm
1×egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049482173
149482173

prune185.0ms (7.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1113114
Fresh033
Picked011
Done011
Total1118119

Merged error: 17.2b

Counts
119 → 8

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.3b
(/ z (sqrt 3.0))

rewrite5.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls

1 calls:

4.0ms
(/ z (sqrt 3.0))

series7.0ms (0.3%)

Counts
1 → 3
Calls

1 calls:

7.0ms
(/ z (sqrt 3.0))

simplify86.0ms (3.4%)

Algorithm
1×egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
04508322
14508322

prune68.0ms (2.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New38442
Fresh055
Picked011
Done022
Total381250

Merged error: 17.2b

Counts
50 → 12

regimes647.0ms (25.3%)

Accuracy

Total 7.2b remaining (27.9%)

Threshold costs 0b (0%)

bsearch32.0ms (1.2%)

Steps
ItersRangePoint
7
2.5788886312504676e+122
1.6970950894039727e+124
1.322520265236586e+124
9
-2.200006954829948e+128
-7.624986842028181e+118
-1.355766780126997e+128

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05134
15134

end0.0ms (0%)

sample551.0ms (21.5%)

Algorithm
1×intervals
Results
379.0ms8000×body80valid

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