Details

Time bar (total: 5.9s)

sample17.0ms

Algorithm
intervals
Results
7.0ms279×body80valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0911
12111
23910
36410
49410
512310
612510
done12510

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.5b
(* y (+ 1.0 (* z z)))
4.3b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 74
Calls
2 calls:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series109.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(* y (+ 1.0 (* z z)))
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify623.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01601102
14171075
21898856
done5000856

prune224.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z))))
4.3b
(/ (/ 1.0 x) (* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (fma z z 1.0))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
6×sqrt-div associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×flip3-+ pow-prod-down flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative hypot-def associate-/l/
Counts
4 → 112
Calls
4 calls:
15.0ms
(* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z))))
17.0ms
(/ (/ 1.0 x) (* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z)))))
1.0ms
(sqrt (fma z z 1.0))
3.0ms
(sqrt (+ 1.0 (* z z)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z))))
86.0ms
(/ (/ 1.0 x) (* (* (sqrt (fma z z 1.0)) y) (sqrt (+ 1.0 (* z z)))))
49.0ms
(sqrt (fma z z 1.0))
46.0ms
(sqrt (+ 1.0 (* z z)))

simplify922.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (210.0ms)

IterNodesCost
02242300
15931964
226771358
done50001358

prune348.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1 (* x (/ (* (fma z z 1.0) y) 1.0)))
3.5b
(* (fma z z 1.0) y)
4.1b
(* x (/ (* (fma z z 1.0) y) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
28×add-cbrt-cube
17×prod-exp
16×div-exp
14×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity associate-*r*
9×cbrt-unprod
8×cbrt-undiv
6×times-frac associate-*l*
4×rec-exp 1-exp
3×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
2×pow-flip associate-*r/ *-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/r/ inv-pow
Counts
3 → 88
Calls
3 calls:
12.0ms
(/ 1 (* x (/ (* (fma z z 1.0) y) 1.0)))
3.0ms
(* (fma z z 1.0) y)
9.0ms
(* x (/ (* (fma z z 1.0) y) 1.0))

series176.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(/ 1 (* x (/ (* (fma z z 1.0) y) 1.0)))
45.0ms
(* (fma z z 1.0) y)
65.0ms
(* x (/ (* (fma z z 1.0) y) 1.0))

simplify1.0s

Counts
97 → 97
Iterations

Useful iterations: 2 (343.0ms)

IterNodesCost
01551331
14031238
21973969
done5000969

prune197.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* (fma z z 1.0) y))
3.5b
(* (fma z z 1.0) y)
4.3b
(/ (/ 1.0 (* (fma z z 1.0) y)) x)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
25×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
10×associate-/l*
7×cbrt-undiv div-exp
6×div-inv
5×pow1
4×associate-/r*
3×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 93
Calls
3 calls:
3.0ms
(/ 1.0 (* (fma z z 1.0) y))
3.0ms
(* (fma z z 1.0) y)
6.0ms
(/ (/ 1.0 (* (fma z z 1.0) y)) x)

series159.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ 1.0 (* (fma z z 1.0) y))
41.0ms
(* (fma z z 1.0) y)
66.0ms
(/ (/ 1.0 (* (fma z z 1.0) y)) x)

simplify670.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
01771418
14251369
218981205
done50011205

prune238.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes243.0ms

Accuracy

0% (1.6b remaining)

Error of 6.2b against oracle of 4.7b and baseline of 6.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01219
11717
21917
done1917

end0.0ms

sample425.0ms

Algorithm
intervals
Results
238.0ms8608×body80valid