Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	231×	pre	80	false

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	101	11
4	198	11
5	376	11
6	618	11
7	1653	11
done	5001	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.1b	(/ (- (* a a) (* b b)) (* a a))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

8.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
22.0ms	(/ (- (* a a) (* b b)) (* a a))

series107.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(- (* a a) (* b b))
19.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
55.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (724.0ms)

Iter	Nodes	Cost
0	99	979
1	230	843
2	698	744
3	3365	735
done	5001	735

prune176.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- a (* b (/ b a))) a)))
0.0b	(/ (- a (* b (/ b a))) a)
0.1b	(* b (/ b a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `sqrt-prod` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 81

Calls

3 calls:

2.0ms	(sqrt (fabs (/ (- a (* b (/ b a))) a)))
14.0ms	(/ (- a (* b (/ b a))) a)
13.0ms	(* b (/ b a))

series88.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(sqrt (fabs (/ (- a (* b (/ b a))) a)))
50.0ms	(/ (- a (* b (/ b a))) a)
22.0ms	(* b (/ b a))

simplify1.7s

Counts

90 → 90

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	138	1060
1	296	997
2	787	912
3	2109	908
done	5000	903

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (log1p (expm1 (/ (- a (* b (/ b a))) a)))))
0.0b	(/ (- a (* b (/ b a))) a)
0.1b	(* b (/ b a))
1.0b	(expm1 (/ (- a (* b (/ b a))) a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-l` `associate-/r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`rem-sqrt-square` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `expm1-udef`

Counts

4 → 92

Calls

4 calls:

1.0ms	(sqrt (fabs (log1p (expm1 (/ (- a (* b (/ b a))) a)))))
14.0ms	(/ (- a (* b (/ b a))) a)
13.0ms	(* b (/ b a))
0.0ms	(expm1 (/ (- a (* b (/ b a))) a))

series152.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (fabs (log1p (expm1 (/ (- a (* b (/ b a))) a)))))
53.0ms	(/ (- a (* b (/ b a))) a)
19.0ms	(* b (/ b a))
64.0ms	(expm1 (/ (- a (* b (/ b a))) a))

simplify1.7s

Counts

104 → 104

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	155	1263
1	326	1156
2	836	1051
3	2244	1046
done	5001	1041

prune311.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (expm1 (log1p (/ (- a (* b (/ b a))) a)))))
0.0b	(expm1 (log1p (/ (- a (* b (/ b a))) a)))
0.0b	(/ (- a (* b (/ b a))) a)
0.1b	(* b (/ b a))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`rem-sqrt-square` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `expm1-udef`

Counts

4 → 92

Calls

4 calls:

1.0ms	(sqrt (fabs (expm1 (log1p (/ (- a (* b (/ b a))) a)))))
0.0ms	(expm1 (log1p (/ (- a (* b (/ b a))) a)))
15.0ms	(/ (- a (* b (/ b a))) a)
13.0ms	(* b (/ b a))

series214.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (fabs (expm1 (log1p (/ (- a (* b (/ b a))) a)))))
121.0ms	(expm1 (log1p (/ (- a (* b (/ b a))) a)))
51.0ms	(/ (- a (* b (/ b a))) a)
23.0ms	(* b (/ b a))

simplify1.6s

Counts

104 → 104

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	159	1274
1	330	1143
2	854	1037
3	2261	1031
done	5001	933

prune312.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample693.0ms

Algorithm

intervals

Results

191.0ms	8000×	body	80	valid
90.0ms	8000×	pre	80	true
87.0ms	8241×	pre	80	false