Details

Time bar (total: 3.0s)

sample30.0ms

Algorithm
intervals
Results
11.0ms280×body80valid
3.0ms93×body80nan

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24414
36514
48914
510214
done10214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.0b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
2.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
11.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
84.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify566.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
01341237
13501139
21742975
done5001975

prune233.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
1.0b
(- (* z z) (* t a))
2.4b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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:
10.0ms
(/ (sqrt (- (* z z) (* t a))) z)
2.0ms
(- (* z z) (* t a))
10.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (sqrt (- (* z z) (* t a))) z)
38.0ms
(- (* z z) (* t a))
85.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify606.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (165.0ms)

IterNodesCost
02102654
15332433
220142221
done50002221

prune369.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
1.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.0b
(- (* z z) (* t a))
22.0b
(sqrt (- (* z z) (* t a)))

rewrite65.0ms

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:
9.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
37.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
3.0ms
(- (* z z) (* t a))
4.0ms
(sqrt (- (* z z) (* t a)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
86.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
34.0ms
(- (* z z) (* t a))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify273.0ms

Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
03304875
18274402