Details

Time bar (total: 2.4m)

sample32.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
4.0ms256×pre80true

simplify489.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
547×*-un-lft-identity
319×add-sqr-sqrt add-cube-cbrt
114×distribute-lft-out
72×associate-/l*
27×div-inv
19×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 404
Calls
3 calls:
40.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
45.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
35.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series601.0ms

Counts
3 → 9
Calls
3 calls:
229.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
249.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
123.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify757.0ms

Counts
413 → 413
Iterations
IterNodes
done5001
11291
0500

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
0.1b
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
0.1b
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.2b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cbrt-cube add-cube-cbrt
28×div-exp
16×associate-*l* prod-exp
15×cbrt-undiv
13×associate-*r*
10×associate-/r*
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×unswap-sqr associate-/l/
5×rec-exp 1-exp div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×frac-times flip3-+ associate-*l/ associate-*r/ associate-/r/ un-div-inv flip-+
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 171
Calls
4 calls:
4.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
42.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
22.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
22.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
226.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
218.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
154.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify493.0ms

Counts
183 → 183
Iterations
IterNodes
done5000
1689
0235

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (fma alpha beta (+ beta alpha)) 1.0)) (fma 2.0 1.0 (+ beta alpha)))
0.5b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
2.2b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.2b
(sqrt (+ (fma alpha beta (+ beta alpha)) 1.0))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
76×sqrt-prod
63×times-frac
58×add-sqr-sqrt
52×add-cube-cbrt
14×associate-/l*
13×distribute-lft-out
9×associate-/r*
8×add-cbrt-cube sqrt-div add-exp-log
6×pow1
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp hypot-def div-inv
1×sqrt-undiv
Counts
4 → 157
Calls
4 calls:
24.0ms
(/ (sqrt (+ (fma alpha beta (+ beta alpha)) 1.0)) (fma 2.0 1.0 (+ beta alpha)))
39.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
12.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
12.0ms
(sqrt (+ (fma alpha beta (+ beta alpha)) 1.0))

series545.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (sqrt (+ (fma alpha beta (+ beta alpha)) 1.0)) (fma 2.0 1.0 (+ beta alpha)))
160.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
65.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
69.0ms
(sqrt (+ (fma alpha beta (+ beta alpha)) 1.0))

simplify938.0ms

Counts
169 → 169
Iterations
IterNodes
done5001
21748
1546
0263

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))))
0.5b
(/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha))))
1.4b
(/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
1.6b
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite9.7s

Algorithm
rewrite-expression-head
Rules
157883×times-frac
83466×*-un-lft-identity
56844×add-sqr-sqrt add-cube-cbrt
26019×sqrt-prod
13311×distribute-lft-out
3932×div-inv
372×associate-/r*
160×add-exp-log
139×div-exp
127×associate-/l*
84×associate-/r/
70×add-cbrt-cube
49×cbrt-undiv
25×1-exp
10×rec-exp
5×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×flip3-+ flip-+
Counts
4 → 30072
Calls
4 calls:
866.0ms
(/ (/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))))
20.0ms
(/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha))))
45.0ms
(/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
22.0ms
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))))
94.0ms
(/ (/ 1 1) (sqrt (fma 2.0 1.0 (+ beta alpha))))
276.0ms
(/ (/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
170.0ms
(/ (+ (fma alpha beta (+ beta alpha)) 1.0) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify14.9s

Counts
30084 → 30084
Iterations
IterNodes
done19651
019651

prune1.9m

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.1b

regimes123.0ms

Accuracy

0% (3.0b remaining)

Error of 4.2b against oracle of 1.3b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done20
120
014

end0.0ms

sample791.0ms

Algorithm
intervals
Results
487.0ms8000×body80valid
100.0ms8000×pre80true