Details

Time bar (total: 8.1s)

analyze1.1s

Algorithm
search

sample33.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms57×body80nan
2.0ms33×body80invalid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.3b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.4b
(* (* x y) z)
9.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
4.0ms
(* (* x y) z)
8.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0343583
11850515
25003510

prune136.0ms

Filtered
60 candidates to 88 candidates (-46.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New781088
Fresh000
Picked101
Done000
Total791089

Merged error: 5.7b

Counts
89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
2.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
4.0ms
(- (* z z) (* t a))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(sqrt (- (* z z) (* t a)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ z (sqrt (- (* z z) (* t a))))
7.0ms
(- (* z z) (* t a))
28.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms
(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04281014
12153912
25002894

prune136.0ms

Filtered
82 candidates to 124 candidates (-51.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1222124
Fresh279
Picked011
Done000
Total12410134

Merged error: 5.4b

Counts
134 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.6b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
21.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
29.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0400774
11768676
25001668

prune121.0ms

Filtered
66 candidates to 104 candidates (-57.6%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1022104
Fresh178
Picked011
Done011
Total10311114

Merged error: 5.4b

Counts
114 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
3.0b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.3b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
4.0ms
(- (* z z) (* t a))
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (sqrt (- (* z z) (* t a))) z)
7.0ms
(- (* z z) (* t a))
32.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
14.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05121325
123581230
250021214

prune104.0ms

Filtered
98 candidates to 144 candidates (-46.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1440144
Fresh088
Picked011
Done022
Total14411155

Merged error: 5.4b

Counts
155 → 11

regimes832.0ms

Accuracy

84.7% (3.0b remaining)

Error of 6.7b against oracle of 3.7b and baseline of 23.3b

bsearch3.1s

Steps
ItersRangePoint
9
2.682616516775416e+108
3.9390808764547876e+115
6.710637687003367e+111
8
-1.977782991384551e+82
-2.614813964780112e+79
-1.5074004949959053e+82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

analyze1.1s

Algorithm
search

sample899.0ms

Algorithm
intervals
Results
418.0ms8000×body80valid
102.0ms2124×body80nan
50.0ms927×body80invalid

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