Details

Time bar (total: 4.1s)

sample29.0ms

Algorithm
intervals
Results
10.0ms279×body80valid
3.0ms106×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
3.0b
(* (* x y) z)
8.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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))
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
96.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
69.0ms
(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25002510

prune249.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
1.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite39.0ms

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:
9.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ z (sqrt (- (* z z) (* t a))))
40.0ms
(- (* z z) (* t a))
95.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04311015
12166912
25002893

prune315.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
0.8b
(- (* z z) (* t a))
1.6b
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
32×add-sqr-sqrt
30×add-cbrt-cube
27×prod-exp
25×associate-*r*
22×times-frac
21×*-un-lft-identity
19×pow1 add-cube-cbrt
15×cbrt-unprod
14×sqrt-prod
9×pow-prod-down
6×div-exp add-log-exp
5×unswap-sqr
4×sqrt-div associate-*r/ associate-*l*
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×associate-/r/ un-div-inv *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 108
Calls
4 calls:
23.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
27.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
38.0ms
(- (* z z) (* t a))
94.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0479962
12408785
25002750

prune282.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.8b
(- (* z z) (* t a))
1.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

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:
8.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
14.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (sqrt (- (* z z) (* t a))) z)
39.0ms
(- (* z z) (* t a))
93.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05191327
123801230
250011214

prune364.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

regimes499.0ms

Accuracy

89.5% (2.0b remaining)

Error of 5.3b against oracle of 3.3b and baseline of 22.4b

bsearch94.0ms

Steps
ItersRangePoint
10
8.756260439201689e+104
1.7016018298191544e+118
1.0315608467704857e+107
5
-3.1723327532004586e+140
-8.095784603387317e+139
-1.5734058117429052e+140

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03128
13228
23828
33828

end0.0ms

sample795.0ms

Algorithm
intervals
Results
331.0ms8836×body80valid
104.0ms2919×body80nan