Details

Time bar (total: 38.7s)

sample64.0ms

Algorithm
intervals
Results
39.0ms256×body80valid
12.0ms256×pre80true

simplify342.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
342.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

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)))

rewrite41.0ms

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:
Slowest
26.0ms
(* (/ b a) (/ b a))
10.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series109.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
57.0ms
(- 1 (* (/ b a) (/ b a)))
27.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.4s

Counts
102 → 118
Calls
102 calls:
Slowest
381.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
211.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
196.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
162.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
153.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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-*r*
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-*l* sqrt-prod
2×associate-*r/ 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:
Slowest
11.0ms
(/ (* b (/ b a)) a)
9.0ms
(* b (/ b a))
8.0ms
(- 1 (/ (* b (/ b a)) a))
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series153.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(- 1 (/ (* b (/ b a)) a))
47.0ms
(/ (* b (/ b a)) a)
24.0ms
(* b (/ b a))
20.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify13.1s

Counts
106 → 132
Calls
106 calls:
Slowest
488.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
417.0ms
(fma 1 1 (- (* (/ (* b (/ b a)) a) 1)))
412.0ms
(fma (- (/ (* b (/ b a)) a)) 1 (* (/ (* b (/ b a)) a) 1))
408.0ms
(fma (- (/ (* b (/ b a)) a)) 1 (* (/ (* b (/ b a)) a) 1))
405.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ (* b (/ b a)) a) 1)))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.3b

localize35.0ms

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))

rewrite50.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 168
Calls
4 calls:
Slowest
25.0ms
(* (/ b a) (/ b a))
18.0ms
(* (/ b a) (/ b a))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
64.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
56.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
46.0ms
(* (/ b a) (/ b a))
45.0ms
(* (/ b a) (/ b a))

simplify8.0s

Counts
168 → 180
Calls
168 calls:
Slowest
435.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
393.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
358.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
328.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
311.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune3.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 7.3b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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
10.0ms
(* b (/ b a))
9.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
1.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
0.0ms
(posit16->real (real->posit16 (* b (/ b a))))

series112.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
34.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
33.0ms
(posit16->real (real->posit16 (* b (/ b a))))
31.0ms
(* b (/ b a))
13.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))

simplify2.5s

Counts
65 → 104
Calls
65 calls:
Slowest
473.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
235.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
169.0ms
(/ (* (* (posit16->real (real->posit16 (* b (/ b a)))) (posit16->real (real->posit16 (* b (/ b a))))) (posit16->real (real->posit16 (* b (/ b a))))) (* (* a a) a))
125.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
123.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune2.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.3b

regimes117.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
883.0ms8000×body80valid
321.0ms8000×pre80true