Details

Time bar (total: 16.3s)

sample70.0ms

Algorithm
intervals
Results
23.0ms283×body80valid
8.0ms98×body80nan

simplify117.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
3.9b
(* (* x y) z)
10.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.2b
(sqrt (- (* z z) (* t a)))

rewrite494.0ms

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:
10.0ms
(- (* z z) (* t a))
31.0ms
(* (* x y) z)
430.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.0ms
(sqrt (- (* z z) (* t a)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* z z) (* t a))
46.0ms
(* (* x y) z)
156.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
96.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
2.4b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
26.2b
(sqrt (- (* z z) (* t a)))

rewrite136.0ms

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:
27.0ms
(/ z (sqrt (- (* z z) (* t a))))
13.0ms
(- (* z z) (* t a))
79.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms
(sqrt (- (* z z) (* t a)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ z (sqrt (- (* z z) (* t a))))
49.0ms
(- (* z z) (* t a))
155.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
87.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
134 → 134
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01792135
14381941
215821740
done50001738

prune559.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(* x (/ z (sqrt (- (* z z) (* t a)))))
0.8b
(- (* z z) (* t a))
1.2b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
26.2b
(sqrt (- (* z z) (* t a)))

rewrite212.0ms

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×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
91.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
19.0ms
(- (* z z) (* t a))
79.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
17.0ms
(sqrt (- (* z z) (* t a)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
41.0ms
(- (* z z) (* t a))
122.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
80.0ms
(sqrt (- (* z z) (* t a)))

simplify2.8s

Counts
114 → 114
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01741680
14141552
212121354
340401340
done50001340

prune420.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt y) (cbrt y))
0.8b
(- (* z z) (* t a))
1.2b
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (* x (/ z (sqrt (- (* z z) (* t a)))))))
26.2b
(sqrt (- (* z z) (* t a)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
33×pow1
23×prod-exp cbrt-unprod
22×add-sqr-sqrt add-cbrt-cube
17×pow-prod-down
16×cbrt-prod
13×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
6×pow1/3 swap-sqr add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*r/ sqrt-prod
2×cbrt-undiv flip3-- sqrt-div div-exp pow-sqr *-commutative pow-prod-up flip--
1×pow2 sub-neg rem-sqrt-square sqrt-pow1 pow-plus pow1/2 fma-neg diff-log prod-diff
Counts
4 → 110
Calls
4 calls:
18.0ms
(* (cbrt y) (cbrt y))
9.0ms
(- (* z z) (* t a))
234.0ms
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (* x (/ z (sqrt (- (* z z) (* t a)))))))
26.0ms
(sqrt (- (* z z) (* t a)))

series699.0ms

Counts
4 → 12
Calls
4 calls:
369.0ms
(* (cbrt y) (cbrt y))
67.0ms
(- (* z z) (* t a))
176.0ms
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (* x (/ z (sqrt (- (* z z) (* t a)))))))
88.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
122 → 122
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01841865
14411729
215931248
done50011131

prune451.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

regimes524.0ms

Accuracy

85.9% (2.8b remaining)

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

bsearch100.0ms

Steps
ItersRangePoint
1
2.7753413219507016e+156
2.949286285521596e+156
2.818827562843425e+156
9
-3.285142281572991e+120
-3.2249995708726854e+115
-5.1997141694493184e+116

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12729
23029
done3029

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s8864×body80valid
245.0ms2951×body80nan