Details

Time bar (total: 14.0s)

sample70.0ms

Algorithm
intervals
Results
24.0ms286×body80valid
5.0ms84×body80nan

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
5.7b
(* (* x y) z)
8.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.0b
(sqrt (- (* z z) (* t a)))

rewrite96.0ms

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:
8.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) z)
55.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* z z) (* t a))
43.0ms
(* (* x y) z)
134.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
92.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
98 → 98
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune407.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
3.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
27.0b
(sqrt (- (* z z) (* t a)))

rewrite91.0ms

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:
27.0ms
(/ (sqrt (- (* z z) (* t a))) z)
8.0ms
(- (* z z) (* t a))
25.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
20.0ms
(sqrt (- (* z z) (* t a)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (sqrt (- (* z z) (* t a))) z)
53.0ms
(- (* z z) (* t a))
112.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
154 → 154
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune560.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.0b
(- (* z z) (* t a))
2.1b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
27.0b
(sqrt (- (* z z) (* t a)))

rewrite113.0ms

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:
18.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
9.0ms
(- (* z z) (* t a))
56.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
17.0ms
(sqrt (- (* z z) (* t a)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
43.0ms
(- (* z z) (* t a))
142.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
86.0ms
(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts
249 → 249
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03424983
18024462
223424239
done50014235

prune905.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (pow z 2) (* a t))))
1.0b
(- (pow z 2) (* a t))
3.2b
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
27.0b
(sqrt (- (pow z 2) (* a t)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×add-cube-cbrt *-un-lft-identity
36×times-frac
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
8×fma-neg prod-diff
6×unpow-prod-down 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 unpow2 sqr-pow
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 136
Calls
4 calls:
38.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
35.0ms
(- (pow z 2) (* a t))
90.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
19.0ms
(sqrt (- (pow z 2) (* a t)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ z (sqrt (- (pow z 2) (* a t))))
59.0ms
(- (pow z 2) (* a t))
117.0ms
(* (* x y) (/ z (sqrt (- (pow z 2) (* a t)))))
76.0ms
(sqrt (- (pow z 2) (* a t)))

simplify1.8s

Counts
148 → 148
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01942307
14712076
216211872
done50011859

prune514.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes390.0ms

Accuracy

85.6% (2.8b remaining)

Error of 6.2b against oracle of 3.4b and baseline of 23.0b

bsearch135.0ms

Steps
ItersRangePoint
9
1.5353641619958244e+124
7.744692910638509e+130
9.92598579242232e+124
9
-1.0828212978382938e+107
-3.015783719596393e+99
-4.610508646786433e+104

simplify17.0ms

Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
02332
13030
23129
34229
done4229

end0.0ms

sample1.5s

Algorithm
intervals
Results
498.0ms8856×body80valid
154.0ms2858×body80nan