Details

sample44.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify275.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

275.0ms

(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.1b

localize24.0ms

Local error

Found 2 expressions with local error:

8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite28.0ms

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

24.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series69.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

48.0ms	(* (/ b a) (/ b a))
21.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.2s

Counts

86 → 88

Calls

86 calls:

Slowest

348.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
202.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
180.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
167.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
121.0ms	(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune824.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 3 expressions with local error:

8.1b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
7.3b	(/ (* (/ b a) b) a)
0.2b	(* (/ b a) b)

rewrite41.0ms

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-l`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-r*` `sqrt-prod` `insert-posit16` `add-log-exp`
2×	`associate-*l/` `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

27.0ms	(/ (* (/ b a) b) a)
11.0ms	(* (/ b a) b)
2.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series85.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

36.0ms	(/ (* (/ b a) b) a)
35.0ms	(* (/ b a) b)
13.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify2.6s

Counts

53 → 81

Calls

53 calls:

Slowest

433.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
262.0ms	(/ (* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b)) (* (* a a) a))
238.0ms	(/ (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* a a) a))
163.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
161.0ms	(/ (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b)) (* (* a a) a))

prune935.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.9b

localize41.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.4b	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))

rewrite56.0ms

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))
23.0ms	(* (/ b a) (/ b a))
1.0ms	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

69.0ms	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
65.0ms	(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
36.0ms	(* (/ b a) (/ b a))
32.0ms	(* (/ b a) (/ b a))

simplify7.5s

Counts

168 → 172

Calls

168 calls:

Slowest

435.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
402.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
318.0ms	(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
292.0ms	(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
281.0ms	(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune2.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.9b

localize33.0ms

Local error

Found 4 expressions with local error:

8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.1b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
13×	`swap-sqr` `associate-r` `associate-l`
9×	`sqrt-prod`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 110

Calls

4 calls:

Slowest

13.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

37.0ms	(* (/ b a) (/ b a))
20.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
18.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
12.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.8s

Counts

102 → 122

Calls

102 calls:

Slowest

430.0ms	(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
237.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
145.0ms	(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
144.0ms	(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
142.0ms	(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))

prune1.7s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.9b

regimes92.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
357.0ms	8000×	pre	80	true