Details

Time bar (total: 10.6s)

sample30.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
7.0ms256×pre80true

simplify739.0ms

Counts
1 → 1
Iterations
IterNodes
done2002
62002
5808
4236
388
244
119
08

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1 (* (/ b a) (/ b a)))
0.4b
(* (/ b a) (/ b a))
6.9b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity
34×add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
5×add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×expm1-log1p-u fma-neg prod-diff sqrt-prod insert-posit16 log1p-expm1-u
2×difference-of-squares
1×pow2 frac-times rem-sqrt-square sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
3 → 109
Calls
3 calls:
10.0ms
(- 1 (* (/ b a) (/ b a)))
28.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series130.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(- 1 (* (/ b a) (/ b a)))
46.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts
118 → 118
Iterations
IterNodes
done2002
32002
21597
1496
0167

prune321.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1 (/ (* (/ b a) b) a))
0.2b
(* (/ b a) b)
6.0b
(/ (* (/ b a) b) a)
6.9b
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
32×*-un-lft-identity
29×add-cube-cbrt
22×times-frac
21×prod-diff
18×add-cbrt-cube add-exp-log
13×associate-*l*
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-*r* sqrt-prod
2×associate-*l/ difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down *-commutative flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
13.0ms
(- 1 (/ (* (/ b a) b) a))
16.0ms
(* (/ b a) b)
11.0ms
(/ (* (/ b a) b) a)
1.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- 1 (/ (* (/ b a) b) a))
20.0ms
(* (/ b a) b)
41.0ms
(/ (* (/ b a) b) a)
23.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify1.1s

Counts
132 → 132
Iterations
IterNodes
done2024
32024
21432
1478
0194

prune604.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 6.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ b a) (sqrt a))
0.3b
(/ (/ b a) (sqrt a))
6.9b
(sqrt (fabs (+ (fma 1 1 (- (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))) (fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a)))))))
52.4b
(fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
282×times-frac
160×add-sqr-sqrt
159×*-un-lft-identity add-cube-cbrt
87×sqrt-prod
26×associate-/l*
16×div-inv
14×add-cbrt-cube add-exp-log
12×associate-/r*
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 257
Calls
4 calls:
14.0ms
(/ (/ b a) (sqrt a))
20.0ms
(/ (/ b a) (sqrt a))
2.0ms
(sqrt (fabs (+ (fma 1 1 (- (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))) (fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a)))))))
0.0ms
(fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ b a) (sqrt a))
83.0ms
(/ (/ b a) (sqrt a))
39.0ms
(sqrt (fabs (+ (fma 1 1 (- (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))) (fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a)))))))
92.0ms
(fma (- (/ b (sqrt a))) (/ (/ b a) (sqrt a)) (* (/ b (sqrt a)) (/ (/ b a) (sqrt a))))

simplify1.1s

Counts
269 → 269
Iterations
IterNodes
done2000
32000
21596
1631
0281

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 6.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ b a) b)
6.0b
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
6.9b
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
46.1b
(posit16->real (real->posit16 (* (/ b a) b)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
13×associate-*l*
11×add-cbrt-cube add-exp-log
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r* sqrt-prod associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative remove-posit16
Counts
4 → 92
Calls
4 calls:
9.0ms
(* (/ b a) b)
4.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
1.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
0.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

series85.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ b a) b)
31.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
12.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
21.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

simplify739.0ms

Counts
104 → 104
Iterations
IterNodes
done2000
32000
2816
1271
0137

prune896.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 6.8b

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done10
110
08

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8000×body80valid
275.0ms8000×pre80true