Details

Time bar (total: 28.6s)

sample54.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
12.0ms256×pre80true

simplify304.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
304.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize12.0ms

Local error

Found 2 expressions with local error:

9.0b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))

rewrite20.0ms

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
17.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series60.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
38.0ms
(* (/ b a) (/ b a))
21.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.4s

Counts
86 → 92
Calls
86 calls:
Slowest
432.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
205.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
148.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
137.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
134.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune916.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.0b

localize39.0ms

Local error

Found 3 expressions with local error:

9.7b
(* (* (/ b a) b) (/ 1 a))
9.0b
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))
0.1b
(* (/ b a) b)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log
29×add-cbrt-cube
25×add-sqr-sqrt
22×prod-exp
19×*-un-lft-identity times-frac add-cube-cbrt
16×associate-*r*
14×associate-*l*
12×cbrt-unprod
11×pow1 div-exp
6×cbrt-undiv
4×pow-prod-down associate-*l/
3×expm1-log1p-u rec-exp 1-exp sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative div-inv unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ un-div-inv
Counts
3 → 100
Calls
3 calls:
Slowest
25.0ms
(* (* (/ b a) b) (/ 1 a))
10.0ms
(* (/ b a) b)
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

series85.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
52.0ms
(* (* (/ b a) b) (/ 1 a))
20.0ms
(* (/ b a) b)
12.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

simplify7.6s

Counts
74 → 109
Calls
74 calls:
Slowest
521.0ms
(sqrt (sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a))))))
483.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))
480.0ms
(fabs (- 1 (* (* (/ b a) b) (/ 1 a))))
443.0ms
(sqrt (* (cbrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a))))) (cbrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))))
353.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.9b

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b
(log (exp (* (/ b a) (/ b a))))
0.4b
(* (/ b a) (/ b a))
0.0b
(exp (* (/ b a) (/ b a)))
0.0b
(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
34×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×pow1 swap-sqr associate-*r* associate-*l*
7×add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv unswap-sqr
3×log-prod log-pow sqrt-prod
2×exp-prod exp-to-pow
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up rem-exp-log
Counts
4 → 116
Calls
4 calls:
Slowest
12.0ms
(* (/ b a) (/ b a))
7.0ms
(log (exp (* (/ b a) (/ b a))))
4.0ms
(exp (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(log (exp (* (/ b a) (/ b a))))
35.0ms
(exp (* (/ b a) (/ b a)))
27.0ms
(* (/ b a) (/ b a))
13.0ms
(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))

simplify4.5s

Counts
101 → 128
Calls
101 calls:
Slowest
409.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
299.0ms
(sqrt (sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a))))))))
299.0ms
(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
275.0ms
(sqrt (* (cbrt (fabs (- 1 (log (exp (* (/ b a) (/ b a))))))) (cbrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))))
252.0ms
(fabs (- 1 (log (exp (* (/ b a) (/ b a))))))

prune1.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 8.9b

localize71.0ms

Local error

Found 4 expressions with local error:

44.2b
(posit16->real (real->posit16 (* (/ b a) b)))
9.7b
(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
9.0b
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
0.1b
(* (/ b a) b)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity
21×times-frac add-cube-cbrt
18×add-exp-log
16×associate-*r* associate-*l*
14×add-cbrt-cube
9×pow1
6×prod-exp
5×unswap-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-exp sqrt-prod
2×cbrt-undiv pow-prod-down *-commutative div-inv
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*l/ associate-*r/ un-div-inv remove-posit16
Counts
4 → 101
Calls
4 calls:
Slowest
12.0ms
(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
9.0ms
(* (/ b a) b)
1.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
1.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
47.0ms
(* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))
33.0ms
(posit16->real (real->posit16 (* (/ b a) b)))
28.0ms
(* (/ b a) b)
12.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))

simplify4.5s

Counts
69 → 113
Calls
69 calls:
Slowest
502.0ms
(sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))
482.0ms
(sqrt (sqrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))))))
475.0ms
(sqrt (* (cbrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))))) (cbrt (fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a)))))))
461.0ms
(fabs (- 1 (* (posit16->real (real->posit16 (* (/ b a) b))) (/ 1 a))))
347.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))

prune2.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.9b

regimes175.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
790.0ms8000×body80valid
395.0ms8000×pre80true