Details

Time bar (total: 27.8s)

sample56.0ms

Algorithm
intervals
Results
30.0ms256×body80valid
12.0ms256×pre80true

simplify265.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
265.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize14.0ms

Local error

Found 3 expressions with local error:

7.4b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity
32×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×sqrt-prod insert-posit16
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 → 97
Calls
3 calls:
Slowest
13.0ms
(* (/ b a) (/ b a))
5.0ms
(- 1 (* (/ b a) (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series99.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
47.0ms
(- 1 (* (/ b a) (/ b a)))
33.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.1s

Counts
94 → 106
Calls
94 calls:
Slowest
445.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
267.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
215.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
164.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
162.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
7.1b
(/ (* (/ b a) b) a)
0.2b
(* (/ b a) b)
0.0b
(- 1 (/ (* (/ b a) b) a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×*-un-lft-identity add-cbrt-cube add-exp-log
15×add-cube-cbrt
13×times-frac associate-*l*
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod insert-posit16
3×associate-/r* associate-*r* sqrt-prod
2×associate-*l/ div-inv 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 → 88
Calls
4 calls:
Slowest
24.0ms
(* (/ b a) b)
22.0ms
(/ (* (/ b a) b) a)
13.0ms
(- 1 (/ (* (/ b a) b) a))
1.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series161.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(- 1 (/ (* (/ b a) b) a))
44.0ms
(/ (* (/ b a) b) a)
33.0ms
(* (/ b a) b)
22.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify3.5s

Counts
62 → 100
Calls
62 calls:
Slowest
397.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
305.0ms
(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
229.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
207.0ms
(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))
207.0ms
(/ (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* a a) a))

prune922.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
7.6b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×cbrt-prod
4×insert-posit16 add-log-exp
2×pow2 frac-times pow-plus pow1/3 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 160
Calls
4 calls:
Slowest
25.0ms
(* (/ b a) (/ b a))
14.0ms
(* (/ b a) (/ b a))
2.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
58.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
29.0ms
(* (/ b a) (/ b a))
28.0ms
(* (/ b a) (/ b a))

simplify8.4s

Counts
168 → 172
Calls
168 calls:
Slowest
564.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
517.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
435.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
399.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
331.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune2.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 7.3b

localize63.0ms

Local error

Found 4 expressions with local error:

46.3b
(posit16->real (real->posit16 (* (/ b a) b)))
7.4b
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
7.1b
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.2b
(* (/ b a) b)

rewrite31.0ms

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×insert-posit16 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 → 84
Calls
4 calls:
Slowest
19.0ms
(* (/ b a) b)
8.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
2.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
1.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

series118.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
39.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
34.0ms
(* (/ b a) b)
32.0ms
(posit16->real (real->posit16 (* (/ b a) b)))
13.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))

simplify2.8s

Counts
65 → 96
Calls
65 calls:
Slowest
433.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
255.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
195.0ms
(/ (* (* (posit16->real (real->posit16 (* (/ b a) b))) (posit16->real (real->posit16 (* (/ b a) b)))) (posit16->real (real->posit16 (* (/ b a) b)))) (* (* a a) a))
141.0ms
(sqrt (* (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a)))) (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))))
107.0ms
(/ (sqrt (posit16->real (real->posit16 (* (/ b a) b)))) (* (cbrt a) (cbrt a)))

prune2.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.3b

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 7.9b against oracle of 7.8b and baseline of 7.9b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
893.0ms8000×body80valid
322.0ms8000×pre80true