Details

Time bar (total: 25.2s)

sample53.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
12.0ms256×pre80true

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
85093
71204
6512
5299
4159
385
243
118
08

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (/ b a) (/ b a))
8.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×times-frac
31×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
10×pow1
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod
2×insert-posit16 add-log-exp
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
2 → 82
Calls
2 calls:
20.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series76.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.0s

Counts
88 → 88
Iterations
IterNodes
34268
21217
1393
0130

prune830.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ b a) b)
7.3b
(* (* (/ b a) b) (/ 1 a))
8.3b
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log
29×add-cbrt-cube
25×add-sqr-sqrt
22×prod-exp
19×*-un-lft-identity times-frac add-cube-cbrt
16×associate-*r*
14×associate-*l*
12×cbrt-unprod
11×pow1 div-exp
6×cbrt-undiv
4×pow-prod-down associate-*l/
3×rec-exp 1-exp sqrt-prod insert-posit16 add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ un-div-inv
Counts
3 → 94
Calls
3 calls:
11.0ms
(* (/ b a) b)
40.0ms
(* (* (/ b a) b) (/ 1 a))
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

series81.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(* (/ b a) b)
27.0ms
(* (* (/ b a) b) (/ 1 a))
19.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

simplify3.2s

Counts
103 → 103
Iterations
IterNodes
34324
21122
1389
0153

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
0.3b
(/ (sqrt b) a)
0.3b
(/ (sqrt b) (/ a b))
8.3b
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
238×add-sqr-sqrt
179×*-un-lft-identity add-cube-cbrt
116×sqrt-prod
83×associate-*l*
32×add-cbrt-cube add-exp-log
22×associate-*r*
17×div-inv
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv div-exp
12×associate-/l*
7×pow1
6×prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
2×clear-num frac-2neg associate-/r/
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 312
Calls
4 calls:
33.0ms
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
6.0ms
(/ (sqrt b) a)
7.0ms
(/ (sqrt b) (/ a b))
1.0ms
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ (sqrt b) (/ a b)) (/ (sqrt b) a))
76.0ms
(/ (sqrt b) a)
101.0ms
(/ (sqrt b) (/ a b))
27.0ms
(sqrt (fabs (- 1 (* (/ (sqrt b) (/ a b)) (/ (sqrt b) a)))))

simplify1.7s

Counts
324 → 324
Iterations
IterNodes
25090
11191
0397

prune3.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt b) a)
0.3b
(/ (sqrt b) (/ a b))
8.3b
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
56.5b
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
98×add-sqr-sqrt
97×*-un-lft-identity add-cube-cbrt
57×sqrt-prod
16×associate-/r*
12×associate-/l*
11×add-cbrt-cube add-exp-log
9×div-inv
5×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ remove-posit16
Counts
4 → 176
Calls
4 calls:
10.0ms
(/ (sqrt b) a)
14.0ms
(/ (sqrt b) (/ a b))
2.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
1.0ms
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (sqrt b) a)
78.0ms
(/ (sqrt b) (/ a b))
17.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (/ (sqrt b) (/ a b)))) (/ (sqrt b) a)))))
77.0ms
(posit16->real (real->posit16 (/ (sqrt b) (/ a b))))

simplify3.0s

Counts
188 → 188
Iterations
IterNodes
36521
21912
1673
0296

prune4.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.2b

regimes89.0ms

Accuracy

0% (0.1b remaining)

Error of 7.4b against oracle of 7.3b and baseline of 7.4b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
210
110
08

end0.0ms

sample1.3s

Algorithm
intervals
Results
815.0ms8000×body80valid
289.0ms8000×pre80true