Details

Time bar (total: 4.0s)

analyze659.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
6.2%82.7%11.1%10
12.5%73.7%13.8%11
15.6%59.5%25%12
17.9%53.3%28.8%13
22.4%47.2%30.4%14

sample26.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
4.0ms96×body80invalid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02113
12113

prune8.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 6.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* z z) t)
0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.7b
(* (* y 4.0) (- (* z z) t))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-cbrt-cube
7×add-log-exp
6×add-sqr-sqrt sub-neg
4×add-cube-cbrt *-un-lft-identity associate-*r*
3×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
2×distribute-rgt-in distribute-lft-in diff-log associate-*r/ associate--r+ difference-of-squares
1×associate-*l* *-commutative
Counts
3 → 48
Calls
3 calls:
4.0ms
(- (* z z) t)
3.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
7.0ms
(* (* y 4.0) (- (* z z) t))

series38.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(- (* z z) t)
22.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
12.0ms
(* (* y 4.0) (- (* z z) t))

simplify38.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05049632

prune85.0ms

Filtered
42 candidates to 57 candidates (-35.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New51657
Fresh000
Picked011
Done000
Total51758

Merged error: 2.0b

Counts
58 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
6.2b
(cbrt (- (* z z) t))
6.2b
(cbrt (- (* z z) t))
6.2b
(cbrt (- (* z z) t))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div associate-*r/
13×pow1 add-exp-log
12×cbrt-prod
11×add-sqr-sqrt add-cbrt-cube
9×flip3-- flip--
8×add-cube-cbrt *-un-lft-identity
6×pow-prod-down prod-exp cbrt-unprod
4×frac-times add-log-exp
3×pow1/3 associate-*l* difference-of-squares
2×associate-*l/
1×associate-*r* *-commutative
Counts
4 → 71
Calls
4 calls:
17.0ms
(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
4.0ms
(cbrt (- (* z z) t))
4.0ms
(cbrt (- (* z z) t))
4.0ms
(cbrt (- (* z z) t))

series80.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
17.0ms
(cbrt (- (* z z) t))
16.0ms
(cbrt (- (* z z) t))
17.0ms
(cbrt (- (* z z) t))

simplify56.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04933935
14933935

prune122.0ms

Filtered
67 candidates to 83 candidates (-23.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New82183
Fresh145
Picked101
Done011
Total84690

Merged error: 2.0b

Counts
90 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
2.0b
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
5.7b
(* y (* 4.0 (- t (* z z))))
5.7b
(* y (* 4.0 (- t (* z z))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×distribute-rgt-in add-cube-cbrt sub-neg *-un-lft-identity distribute-lft-in associate-*r/
6×associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×sqrt-div add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*r* *-commutative flip-- flip-+
Counts
4 → 78
Calls
4 calls:
3.0ms
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
3.0ms
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
6.0ms
(* y (* 4.0 (- t (* z z))))
7.0ms
(* y (* 4.0 (- t (* z z))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
38.0ms
(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
15.0ms
(* y (* 4.0 (- t (* z z))))
16.0ms
(* y (* 4.0 (- t (* z z))))

simplify49.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
055061142

prune128.0ms

Filtered
62 candidates to 90 candidates (-45.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New90090
Fresh044
Picked011
Done011
Total90696

Merged error: 2.0b

Counts
96 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (- (pow z 4) (* t t)))
3.1b
(- (pow z 4) (* t t))
8.6b
(* y (* 4.0 (- (pow z 4) (* t t))))
21.6b
(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
15×add-sqr-sqrt
11×pow1
10×associate-*r/
9×add-cube-cbrt *-un-lft-identity
7×sub-neg associate-*r* prod-exp cbrt-unprod
6×associate-*l* add-log-exp difference-of-squares
5×distribute-rgt-in distribute-lft-in
4×flip3-- pow-prod-down flip--
3×cbrt-undiv times-frac div-exp associate-/r*
2×unpow-prod-down associate-/r/ *-commutative associate-/l/ sqr-pow
1×frac-2neg flip3-+ diff-log clear-num flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 90
Calls
4 calls:
7.0ms
(* 4.0 (- (pow z 4) (* t t)))
4.0ms
(- (pow z 4) (* t t))
8.0ms
(* y (* 4.0 (- (pow z 4) (* t t))))
11.0ms
(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

series72.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* 4.0 (- (pow z 4) (* t t)))
6.0ms
(- (pow z 4) (* t t))
21.0ms
(* y (* 4.0 (- (pow z 4) (* t t))))
37.0ms
(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

simplify39.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
053041154

prune111.0ms

Filtered
66 candidates to 102 candidates (-54.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1020102
Fresh033
Picked011
Done022
Total1026108

Merged error: 2.0b

Counts
108 → 6

regimes862.0ms

Accuracy

80.8% (0.6b remaining)

Error of 3.3b against oracle of 2.7b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02736
12736

end0.0ms

analyze651.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
6.2%82.7%11.1%10
12.5%73.7%13.8%11
15.6%59.5%25%12
17.9%53.3%28.8%13
22.4%47.2%30.4%14

sample696.0ms

Algorithm
intervals
Results
306.0ms8000×body80valid
121.0ms3061×body80invalid

Profiling

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