Details

Time bar (total: 6.7s)

sample30.0ms

Algorithm
intervals
Results
7.0ms272×body80valid
6.0ms233×body80nan

simplify18.0ms

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

localize7.0ms

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)

series133.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(fma (sqrt z) y x)
71.0ms
(/ (* (fma (sqrt z) y x) 1.0) 2.0)

simplify102.0ms

Counts
39 → 39
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0191219
1691184
23882184
35001176
done5001176

prune96.0ms

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))

rewrite25.0ms

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)
14.0ms
(/ 1 (/ 2.0 (* (fma (sqrt z) y x) 1.0)))
7.0ms
(/ 2.0 (* (fma (sqrt z) y x) 1.0))

series245.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(fma (sqrt z) y x)
74.0ms
(/ 1 (/ 2.0 (* (fma (sqrt z) y x) 1.0)))
108.0ms
(/ 2.0 (* (fma (sqrt z) y x) 1.0))

simplify46.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0350691
11582590
25001551
done5001551

prune185.0ms

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))

rewrite81.0ms

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)
31.0ms
(/ 1 (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0)))
34.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0))
9.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

series843.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma (sqrt z) y x)
293.0ms
(/ 1 (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0)))
299.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt 2.0) 1.0))
186.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

simplify72.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06681632
131751325
250021313
done50021313

prune394.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
217×sqrt-prod
196×add-exp-log
182×add-sqr-sqrt
179×times-frac
116×associate-*r*
112×add-cbrt-cube
108×add-cube-cbrt *-un-lft-identity
79×div-exp
76×prod-exp
42×cbrt-undiv
40×cbrt-unprod
23×associate-*l*
21×unswap-sqr
17×pow1
11×frac-times rec-exp 1-exp associate-*l/
9×associate-/l*
7×associate-*r/ pow-prod-down associate-/r/
5×div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×pow-flip
2×frac-2neg clear-num *-commutative
1×inv-pow
Counts
4 → 336
Calls
4 calls:
158.0ms
(/ 1 (* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))))
57.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0)))
95.0ms
(* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))) (/ (sqrt (sqrt 2.0)) (sqrt 1.0)))
6.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

series2.2s

Counts
4 → 12
Calls
4 calls:
496.0ms
(/ 1 (* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))))
742.0ms
(* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0)))
729.0ms
(* (* (/ (sqrt 2.0) (fma (sqrt z) y x)) (/ (sqrt (sqrt 2.0)) (sqrt 1.0))) (/ (sqrt (sqrt 2.0)) (sqrt 1.0)))
184.0ms
(/ (sqrt 2.0) (fma (sqrt z) y x))

simplify64.0ms

Counts
348 → 348
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012525110
150014171
done50014171

prune792.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes119.0ms

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

sample894.0ms

Algorithm
intervals
Results
221.0ms8576×body80valid
206.0ms8413×body80nan