Details

Time bar (total: 6.4s)

sample30.0ms

Algorithm
intervals
Results
7.0ms272×body80valid
6.0ms233×body80nan

simplify19.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1514
2864
31264
41514
51694
61854
71874
81874
done1874

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sqrt z) y x)
0.2b
(/ (* (fma (sqrt z) y x) 1.0) 2.0)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log add-cbrt-cube
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×times-frac associate-/r*
2×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
1×frac-2neg prod-exp clear-num cbrt-unprod fma-udef div-inv associate-/l*
Counts
2 → 33
Calls
2 calls:
0.0ms
(fma (sqrt z) y x)
10.0ms
(/ (* (fma (sqrt z) y x) 1.0) 2.0)

series140.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(fma (sqrt z) y x)
78.0ms
(/ (* (fma (sqrt z) y x) 1.0) 2.0)

simplify104.0ms

Counts
39 → 39
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
0191219
1691184
23882184
35001176
done5001176

prune105.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(fma (sqrt z) y x)
0.2b
(/ 1 (/ 2.0 (* (fma (sqrt z) y x) 1.0)))
0.4b
(/ 2.0 (* (fma (sqrt z) y x) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
29×add-exp-log
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
14×div-exp
8×associate-/r*
7×cbrt-undiv
6×div-inv associate-/l*
4×pow1 prod-exp
3×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num cbrt-unprod
1×pow-flip associate-/r/ fma-udef inv-pow
Counts
3 → 91
Calls
3 calls:
0.0ms
(fma (sqrt z) y x)
17.0ms
(/ 1 (/ 2.0 (* (fma (sqrt z) y x) 1.0)))
7.0ms
(/ 2.0 (* (fma (sqrt z) y x) 1.0))

series241.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(fma (sqrt z) y x)
71.0ms
(/ 1 (/ 2.0 (* (fma (sqrt z) y x) 1.0)))
112.0ms
(/ 2.0 (* (fma (sqrt z) y x) 1.0))

simplify44.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0350691
11582590
25001551
done5001551

prune387.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sqrt z) y x)
0.2b
(/ 1 (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0)))
0.4b
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0))
0.7b
(/ (sqrt 2.0) (fma (sqrt z) y x))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt
69×times-frac
62×add-exp-log
47×add-cube-cbrt *-un-lft-identity
36×sqrt-prod add-cbrt-cube
27×div-exp
22×associate-*r* associate-*l*
16×prod-exp
14×cbrt-undiv
9×pow1 associate-/l* unswap-sqr
8×cbrt-unprod
5×rec-exp 1-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp
3×associate-/r/
2×frac-times pow-flip frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num
1×*-commutative fma-udef inv-pow
Counts
4 → 171
Calls
4 calls:
0.0ms
(fma (sqrt z) y x)
29.0ms
(/ 1 (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0)))
36.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0))
6.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

series838.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma (sqrt z) y x)
291.0ms
(/ 1 (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0)))
289.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0))
193.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

simplify79.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06681632
131751325
250021313
done50021313

prune423.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0))))
0.3b
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0)))
0.3b
(* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0)))
0.7b
(/ (sqrt 2.0) (fma (sqrt z) y x))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
99×sqrt-prod
89×times-frac
62×add-cube-cbrt *-un-lft-identity
54×add-exp-log
50×associate-*r*
34×add-cbrt-cube
23×associate-*l*
22×prod-exp
18×sqrt-div
17×pow1
14×div-exp
12×cbrt-unprod unswap-sqr
11×frac-times associate-*l/
9×associate-/l*
8×cbrt-undiv
7×associate-*r/ pow-prod-down associate-/r/
5×div-inv
4×expm1-log1p-u rec-exp 1-exp associate-/r* log1p-expm1-u add-log-exp
3×pow-flip
2×frac-2neg clear-num *-commutative
1×inv-pow
Counts
4 → 215
Calls
4 calls:
124.0ms
(/ 1 (* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0))))
38.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0)))
71.0ms
(* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0)))
9.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

series1.9s

Counts
4 → 12
Calls
4 calls:
581.0ms
(/ 1 (* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0))))
556.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0)))
559.0ms
(* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (sqrt (/ (sqrt 2.0) 1.0))) (sqrt (/ (sqrt 2.0) 1.0)))
184.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

simplify86.0ms

Counts
227 → 227
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07352628
137022182
250022126
done50022126

prune584.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes138.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0104
1104
done104

end0.0ms

sample884.0ms

Algorithm
intervals
Results
224.0ms8576×body80valid
207.0ms8413×body80nan