Details

Time bar (total: 4.3s)

sample33.0ms

Algorithm
intervals
Results
13.0ms279×body80valid
4.0ms106×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize11.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series205.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551

prune277.0ms

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)))

rewrite35.0ms

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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
6.0ms
(/ 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)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ z (sqrt (- (* z z) (* t a))))
33.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04531067
12239963
25001942

prune346.0ms

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×expm1-log1p-u sqrt-div associate-*r/ associate-*l* log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 118
Calls
4 calls:
20.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
3.0ms
(- (* z z) (* t a))
30.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* z (/ 1 (sqrt (- (* z z) (* t a)))))
32.0ms
(- (* z z) (* t a))
83.0ms
(* (* x y) (* z (/ 1 (sqrt (- (* z z) (* t a))))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05011017
12458840
25002802

prune322.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize11.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
7.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
8.0ms
(sqrt (- (* z z) (* t a)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (sqrt (- (* z z) (* t a))) z)
38.0ms
(- (* z z) (* t a))
80.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05431379
124481281
250011260

prune578.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

regimes468.0ms

Accuracy

89.5% (2.0b remaining)

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

bsearch90.0ms

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
03228
13828
23828

end0.0ms

sample823.0ms

Algorithm
intervals
Results
348.0ms8836×body80valid
106.0ms2919×body80nan