Details

Time bar (total: 20.2s)

sample42.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
8.0ms256×pre80true

simplify231.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
231.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize24.0ms

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×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:
Slowest
29.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series66.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
44.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.4s

Counts
86 → 88
Calls
86 calls:
Slowest
461.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
233.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
165.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
134.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
130.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune756.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.2b

localize21.0ms

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))

rewrite22.0ms

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×associate-/r* associate-*l* sqrt-prod insert-posit16 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 → 72
Calls
3 calls:
Slowest
12.0ms
(/ (* b (/ b a)) a)
8.0ms
(* b (/ b a))
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series72.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
34.0ms
(/ (* b (/ b a)) a)
23.0ms
(* b (/ b a))
15.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify3.1s

Counts
53 → 81
Calls
53 calls:
Slowest
935.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
241.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
208.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
204.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
178.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))

prune781.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.1b

localize34.0ms

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))

rewrite55.0ms

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×sqrt-prod insert-posit16 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 diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
3 → 55
Calls
3 calls:
Slowest
37.0ms
(/ (- (* a a) (* b b)) (* a a))
15.0ms
(- (* a a) (* b b))
2.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

series168.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
92.0ms
(/ (- (* a a) (* b b)) (* a a))
51.0ms
(- (* a a) (* b b))
25.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

simplify4.3s

Counts
35 → 64
Calls
35 calls:
Slowest
293.0ms
(sqrt (* (cbrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (cbrt (fabs (/ (- (* a a) (* b b)) (* a a))))))
293.0ms
(/ (* (* (- (* a a) (* b b)) (- (* a a) (* b b))) (- (* a a) (* b b))) (* (* (* a a) (* a a)) (* a a)))
276.0ms
(- (* (* a a) (* a a)) (* (* b b) (* b b)))
262.0ms
(fabs (/ (- (* a a) (* b b)) (* a a)))
242.0ms
(sqrt (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))

prune586.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.1b

localize60.0ms

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))

rewrite28.0ms

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×insert-posit16 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 → 84
Calls
4 calls:
Slowest
16.0ms
(* b (/ b a))
7.0ms
(/ (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))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
29.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
28.0ms
(posit16->real (real->posit16 (* b (/ b a))))
19.0ms
(* b (/ b a))
14.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))

simplify2.5s

Counts
65 → 96
Calls
65 calls:
Slowest
479.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
199.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
183.0ms
(/ (* (* (posit16->real (real->posit16 (* b (/ b a)))) (posit16->real (real->posit16 (* b (/ b a))))) (posit16->real (real->posit16 (* b (/ b a))))) (* (* a a) a))
124.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
113.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune2.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.1b

regimes411.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
841.0ms8000×body80valid
388.0ms8000×pre80true