Details

Time bar (total: 15.0s)

sample46.0ms

Algorithm
intervals
Results
17.0ms288×body80valid
4.0ms72×body80nan

simplify101.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.8b
(* (* x y) z)
9.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite91.0ms

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:
8.0ms
(- (* z z) (* t a))
19.0ms
(* (* x y) z)
46.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
15.0ms
(sqrt (- (* z z) (* t a)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* z z) (* t a))
37.0ms
(* (* x y) z)
130.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
110.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
88 → 88
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune323.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- (* z z) (* t a))) z)
0.2b
(- (* z z) (* t a))
2.8b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite106.0ms

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:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
22.0ms
(- (* z z) (* t a))
44.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
17.0ms
(sqrt (- (* z z) (* t a)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (sqrt (- (* z z) (* t a))) z)
60.0ms
(- (* z z) (* t a))
156.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts
144 → 144
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02102654
15752439
237182239
done50002233

prune503.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
1.2b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite169.0ms

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×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 diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 227
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
40.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
94.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
13.0ms
(sqrt (- (* z z) (* t a)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* z z) (* t a))
91.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
148.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify614.0ms

Counts
239 → 239
Iterations

Useful iterations: done (601.0ms)

IterNodesCost
03304875
19554438
done50014180

prune885.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
1.1b
(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
2.2b
(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
24.9b
(sqrt (- (* z z) (* t a)))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
268×times-frac
166×add-sqr-sqrt
147×*-un-lft-identity
144×add-cube-cbrt
72×associate-*r*
68×sqrt-prod
62×add-exp-log
32×add-cbrt-cube
22×prod-exp associate-/r*
21×div-exp
13×pow1
10×cbrt-unprod
9×cbrt-undiv div-inv
7×unswap-sqr
6×rec-exp 1-exp associate-*l*
4×associate-*r/ pow-prod-down add-log-exp
3×associate-/l*
2×sqrt-div associate-/r/ un-div-inv *-commutative
1×rem-sqrt-square flip3-- pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num flip-- inv-pow
Counts
4 → 257
Calls
4 calls:
39.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
87.0ms
(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
137.0ms
(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
18.0ms
(sqrt (- (* z z) (* t a)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) z))
82.0ms
(* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z)))
116.0ms
(* x (* y (/ 1 (/ (sqrt (- (* z z) (* t a))) z))))
100.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
269 → 269
Iterations

Useful iterations: 2 (781.0ms)

IterNodesCost
03365539
19784642
242414138
done50014138

prune837.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes589.0ms

Accuracy

84.2% (3.1b remaining)

Error of 6.4b against oracle of 3.3b and baseline of 22.9b

bsearch136.0ms

Steps
ItersRangePoint
8
1.473270777738138e+80
6.009375374018846e+83
6.239560565980057e+82
7
-6.537164733756459e+138
-2.8278494132354943e+136
-8.271419220344132e+137

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02231
13231
23431
done3431

end0.0ms

sample2.4s

Algorithm
intervals
Results
717.0ms8817×body80valid
218.0ms2946×body80nan