Details

Time bar (total: 4.8s)

sample32.0ms

Algorithm
intervals
Results
10.0ms287×body80valid
3.0ms93×body80nan

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207
done1207

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
5.6b
(* (* x y) z)
8.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite70.0ms

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:
9.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
28.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
15.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
93.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0368630
11941560
25001551
done5001551

prune274.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
3.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite63.0ms

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:
17.0ms
(/ (sqrt (- (* z z) (* t a))) z)
11.0ms
(- (* z z) (* t a))
20.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
11.0ms
(sqrt (- (* z z) (* t a)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (sqrt (- (* z z) (* t a))) z)
40.0ms
(- (* z z) (* t a))
89.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify66.0ms

Counts
154 → 154
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05431379
124481281
250011260
done50011260

prune400.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.5b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative
Counts
4 → 237
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
16.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
51.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
11.0ms
(sqrt (- (* z z) (* t a)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* z z) (* t a))
63.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
95.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify103.0ms

Counts
249 → 249
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08392556
140712400
250022396
done50022396

prune645.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
3.8b
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
49×add-sqr-sqrt
48×add-cube-cbrt *-un-lft-identity
44×unpow-prod-down
33×sqrt-prod
29×associate-/r*
26×add-exp-log
11×div-exp add-cbrt-cube
7×associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div pow-exp prod-exp log1p-expm1-u div-inv
3×cbrt-undiv flip3-- flip--
2×pow-to-exp frac-2neg clear-num associate-/l/ sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff cbrt-unprod
Counts
4 → 151
Calls
4 calls:
16.0ms
(/ (sqrt (- (* z z) (* t a))) z)
11.0ms
(- (* z z) (* t a))
33.0ms
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
11.0ms
(sqrt (- (* z z) (* t a)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (sqrt (- (* z z) (* t a))) z)
36.0ms
(- (* z z) (* t a))
91.0ms
(/ (* x y) (pow (/ (sqrt (- (* z z) (* t a))) z) 1))
65.0ms
(sqrt (- (* z z) (* t a)))

simplify69.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06031536
127211342
250011332
done50011332

prune413.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

regimes396.0ms

Accuracy

86% (2.8b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 23.2b

bsearch78.0ms

Steps
ItersRangePoint
9
3.0509751148851044e+144
4.046094989899507e+150
1.874715117526438e+146
8
-1.693909364183909e+121
-1.1368421250931169e+117
-6.341587143310156e+119

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02610
13210
23210
done3210

end0.0ms

sample898.0ms

Algorithm
intervals
Results
319.0ms8900×body80valid
94.0ms2959×body80nan