Details

Time bar (total: 11.2s)

analyze1.2s

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
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.3%0.2%12
12.2%87.5%0.2%13
21.9%77.7%0.4%14

sample28.0ms

Algorithm
intervals
Results
8.0ms212×body80valid
2.0ms15×body640valid
1.0ms36×body80invalid
1.0ms12×body320valid
1.0ms12×body160valid
1.0ms4×body1280valid
0.0ms1×body2560valid

simplify108.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (106.0ms)

IterNodesCost
0507813

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.5b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.6b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.1b
(* (- y z) (/ (- t x) (- a z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 119
Calls
3 calls:
7.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series104.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- t x) (- a z))
54.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
37.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify50.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
056461598

prune180.0ms

Filtered
88 candidates to 128 candidates (-45.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11513128
Fresh000
Picked101
Done000
Total11613129

Merged error: 4.7b

Counts
129 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.0b
(* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z))))))
8.5b
(+ x (* (* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
16×frac-times cbrt-div
14×flip3-- flip--
13×add-sqr-sqrt *-un-lft-identity
11×add-cbrt-cube
10×cbrt-prod
9×pow1
8×associate-*r/ associate-*l/ prod-exp cbrt-unprod
7×add-cube-cbrt
6×add-log-exp
5×associate-*l*
3×pow-prod-down distribute-lft-out-- difference-of-squares
2×cbrt-undiv pow1/3 div-exp
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+
Counts
4 → 82
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
24.0ms
(* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms
(+ x (* (* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series234.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt (- a z))
27.0ms
(cbrt (- a z))
127.0ms
(* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z))))))
53.0ms
(+ x (* (* (- y z) (* (cbrt (- t x)) (/ (cbrt (- t x)) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049851578
149851578

prune173.0ms

Filtered
75 candidates to 94 candidates (-25.3%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New92294
Fresh01212
Picked011
Done000
Total9215107

Merged error: 4.7b

Counts
107 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
2.4b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.2b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 134
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
34.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt (- a z))
27.0ms
(cbrt (- a z))
61.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
55.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049572493
149572493

prune183.0ms

Filtered
107 candidates to 146 candidates (-36.4%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1442146
Fresh21113
Picked011
Done011
Total14615161

Merged error: 4.7b

Counts
161 → 15

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
1.6b
(* (/ (- y z) (- a z)) (- t x))
2.9b
(+ x (pow (* (/ (- y z) (- a z)) (- t x)) 1))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×associate-*l*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*r* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
2×cbrt-undiv frac-times sub-neg associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in flip3-+ div-sub pow-prod-down associate-*l/ clear-num sum-log *-commutative flip-+ distribute-lft-out
Counts
3 → 122
Calls
3 calls:
7.0ms
(/ (- y z) (- a z))
15.0ms
(* (/ (- y z) (- a z)) (- t x))
4.0ms
(+ x (pow (* (/ (- y z) (- a z)) (- t x)) 1))

series120.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(/ (- y z) (- a z))
56.0ms
(* (/ (- y z) (- a z)) (- t x))
53.0ms
(+ x (pow (* (/ (- y z) (- a z)) (- t x)) 1))

simplify50.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
055351659

prune122.0ms

Filtered
89 candidates to 131 candidates (-47.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1292131
Fresh21012
Picked101
Done112
Total13313146

Merged error: 4.7b

Counts
146 → 13

regimes591.0ms

Accuracy

4.4% (7.9b remaining)

Error of 11.3b against oracle of 3.4b and baseline of 11.7b

bsearch5.7s

Steps
ItersRangePoint
9
5.703898425749918e-79
8.09052430801213e-72
7.830320865923943e-79
10
2.2218388159259802e-126
1.1337893443539547e-116
1.429293235495582e-120
9
1.1383484440876772e-233
3.2617597085426898e-226
4.3767089752423955e-228
7
6.393033257476007e-273
1.7117671862617553e-271
3.2726115206355276e-272

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04567
14567

end0.0ms

analyze1.0s

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
0%99.8%0.2%9
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.3%0.2%12
12.2%87.5%0.2%13
21.9%77.7%0.4%14

sample778.0ms

Algorithm
intervals
Results
258.0ms6549×body80valid
70.0ms498×body640valid
53.0ms270×body1280valid
51.0ms1302×body80invalid
49.0ms406×body320valid
19.0ms260×body160valid
4.0ms17×body2560valid

Profiling

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