Details

Time bar (total: 31.0s)

sample53.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
12.0ms256×pre80true

simplify289.0ms

Calls
1 calls:
Slowest
289.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 3 expressions with local error:

6.0b
(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--
Calls
3 calls:
Slowest
25.0ms
(* (/ b a) (/ b a))
10.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series106.0ms

Calls
3 calls:
Slowest
55.0ms
(- 1 (* (/ b a) (/ b a)))
27.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.4s

Calls
102 calls:
Slowest
387.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
261.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
258.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
180.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
155.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* b (/ b a)) a)
6.0b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.2b
(* b (/ b a))
0.0b
(- 1 (/ (* b (/ b a)) a))

rewrite61.0ms

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/
Calls
4 calls:
Slowest
21.0ms
(/ (* b (/ b a)) a)
18.0ms
(- 1 (/ (* b (/ b a)) a))
16.0ms
(* b (/ b a))
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series154.0ms

Calls
4 calls:
Slowest
45.0ms
(/ (* b (/ b a)) a)
44.0ms
(- 1 (/ (* b (/ b a)) a))
36.0ms
(* b (/ b a))
28.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify12.8s

Calls
106 calls:
Slowest
584.0ms
(fma (- (cbrt (/ (* b (/ b a)) a))) (* (cbrt (/ (* b (/ b a)) a)) (cbrt (/ (* b (/ b a)) a))) (* (cbrt (/ (* b (/ b a)) a)) (* (cbrt (/ (* b (/ b a)) a)) (cbrt (/ (* b (/ b a)) a)))))
455.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
383.0ms
(fma (sqrt 1) (sqrt 1) (- (* (/ (* b (/ b a)) a) 1)))
381.0ms
(fma (- (/ (* b (/ b a)) a)) 1 (* (/ (* b (/ b a)) a) 1))
368.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ (* b (/ b a)) a) 1)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 5.8b

localize20.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* b (/ b a)) a)
6.4b
(/ (* b (/ b a)) a)
6.0b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.0b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
6×pow1 associate-/r* times-frac sqrt-prod
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ div-inv associate-/l* associate-/l/
Calls
4 calls:
Slowest
23.0ms
(/ (* b (/ b a)) a)
10.0ms
(/ (* b (/ b a)) a)
3.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series103.0ms

Calls
4 calls:
Slowest
46.0ms
(/ (* b (/ b a)) a)
32.0ms
(/ (* b (/ b a)) a)
12.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
12.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify3.2s

Calls
52 calls:
Slowest
242.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
230.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
193.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
190.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))
181.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 5.8b

localize86.0ms

Local error

Found 4 expressions with local error:

48.8b
(posit16->real (real->posit16 (* b (/ b a))))
6.4b
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
6.0b
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
0.2b
(* b (/ b a))

rewrite31.0ms

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
Calls
4 calls:
Slowest
17.0ms
(* b (/ b a))
9.0ms
(/ (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))))

series119.0ms

Calls
4 calls:
Slowest
43.0ms
(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
35.0ms
(posit16->real (real->posit16 (* b (/ b a))))
24.0ms
(* b (/ b a))
17.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))

simplify2.3s

Calls
65 calls:
Slowest
423.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
162.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
142.0ms
(/ (* (* (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 (/ (pow b 2) (pow a 2)))))
102.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))

prune2.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes182.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
863.0ms8000×body80valid
327.0ms8000×pre80true