Details

sample36.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5216
6	2493
5	808
4	236
3	88
2	44
1	19
0	8

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

localize27.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite21.0ms

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:

17.0ms	(* (/ b a) (/ b a))
3.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series57.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	4044
2	1310
1	407
0	134

prune318.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* b (/ b a))
7.2b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.2b	(/ (* b (/ b a)) a)

rewrite38.0ms

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-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `associate-l*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/` `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 → 78

Calls

3 calls:

20.0ms	(* b (/ b a))
2.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
15.0ms	(/ (* b (/ b a)) a)

series65.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(* b (/ b a))
13.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
32.0ms	(/ (* b (/ b a)) a)

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1053
1	293
0	122

prune441.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))
7.2b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
11.6b	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `cube-unmult` `rem-cbrt-cube`

Counts

4 → 169

Calls

4 calls:

12.0ms	(* (/ b a) (/ b a))
25.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.0ms	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ b a) (/ b a))
45.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
14.0ms	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))

simplify3.2s

Counts

181 → 181

Iterations

Iter	Nodes
done	5464
3	4135
2	1420
1	427
0	146

prune799.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
7.2b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
21.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `prod-exp` `cbrt-unprod` `div-inv`

Counts

3 → 63

Calls

3 calls:

17.0ms	(- (* a a) (* b b))
2.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
42.0ms	(/ (- (* a a) (* b b)) (* a a))

series147.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(- (* a a) (* b b))
26.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
74.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify3.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	4982
2	799
1	256
0	102

prune323.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.0b

regimes373.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
285.0ms	8000×	pre	80	true