Details

Time bar (total: 22.8s)

sample44.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
10.0ms256×pre80true

simplify343.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
343.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize15.0ms

Local error

Found 2 expressions with local error:

9.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))

rewrite33.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 86
Calls
2 calls:
Slowest
27.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
31.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.8s

Counts
86 → 92
Calls
86 calls:
Slowest
489.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
226.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
191.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
152.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
147.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune861.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.2b

localize15.0ms

Local error

Found 3 expressions with local error:

9.3b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.2b
(/ (* b (/ b a)) a)
0.2b
(* b (/ b a))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
17×add-cbrt-cube add-exp-log
14×*-un-lft-identity add-cube-cbrt
13×times-frac associate-*r*
6×pow1
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod
3×expm1-log1p-u associate-/r* associate-*l* sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
2×associate-*r/ div-inv unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative associate-/l* associate-/l/
Counts
3 → 78
Calls
3 calls:
Slowest
11.0ms
(/ (* b (/ b a)) a)
9.0ms
(* b (/ b a))
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series102.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
46.0ms
(/ (* b (/ b a)) a)
34.0ms
(* b (/ b a))
23.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify2.8s

Counts
53 → 87
Calls
53 calls:
Slowest
448.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
267.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
236.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
190.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
171.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))

prune873.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.1b

localize33.0ms

Local error

Found 3 expressions with local error:

20.9b
(/ (- (* a a) (* b b)) (* a a))
9.3b
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b
(- (* a a) (* b b))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
8×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×add-log-exp
4×pow1 times-frac associate-/l*
3×expm1-log1p-u sqrt-prod insert-posit16 log1p-expm1-u difference-of-squares
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff prod-exp cbrt-unprod div-inv
Counts
3 → 63
Calls
3 calls:
Slowest
38.0ms
(/ (- (* a a) (* b b)) (* a a))
21.0ms
(- (* a a) (* b b))
2.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

series133.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
68.0ms
(/ (- (* a a) (* b b)) (* a a))
51.0ms
(- (* a a) (* b b))
15.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

simplify5.3s

Counts
37 → 72
Calls
37 calls:
Slowest
366.0ms
(/ (* (* (- (* a a) (* b b)) (- (* a a) (* b b))) (- (* a a) (* b b))) (* (* (* a a) (* a a)) (* a a)))
346.0ms
(sqrt (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))
309.0ms
(/ (* (* (- (* a a) (* b b)) (- (* a a) (* b b))) (- (* a a) (* b b))) (* (* (* a a) a) (* (* a a) a)))
304.0ms
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
294.0ms
(sqrt (* (cbrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (cbrt (fabs (/ (- (* a a) (* b b)) (* a a))))))

prune673.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.1b

localize46.0ms

Local error

Found 4 expressions with local error:

45.7b
(posit16->real (real->posit16 (* b (/ b a))))
9.3b
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
7.2b
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
0.2b
(* b (/ b a))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
13×associate-*r*
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-*l* 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-*r/ *-commutative remove-posit16
Counts
4 → 92
Calls
4 calls:
Slowest
18.0ms
(* b (/ b a))
13.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
2.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
1.0ms
(posit16->real (real->posit16 (* b (/ b a))))

series139.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
38.0ms
(* b (/ b a))
34.0ms
(posit16->real (real->posit16 (* b (/ b a))))
22.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))

simplify2.8s

Counts
65 → 104
Calls
65 calls:
Slowest
550.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
234.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
140.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
133.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
130.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune2.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.1b

regimes495.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
343.0ms8000×pre80true