Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	217×	pre	80	false

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	100	11
4	190	11
5	330	11
6	557	11
7	1628	11
done	5000	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

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))))
13.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms

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:

3.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

series103.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(- (* a a) (* b b))
20.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
51.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify660.0ms

Counts

69 → 69

Iterations

Useful iterations: done (658.0ms)

Iter	Nodes	Cost
0	99	979
1	236	843
2	840	744
done	5001	736

prune183.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (* (/ b a) b))
0.0b	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
0.0b	(/ 1 (/ a (- a (* (/ b a) b))))
0.1b	(* (/ b a) b)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
65×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
15×	`associate-/r*`
14×	`add-cbrt-cube`
13×	`associate-l`
9×	`associate-/r/`
8×	`pow1` `div-exp`
6×	`div-inv` `add-log-exp`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `sqrt-prod` `associate-/l*`
2×	`rec-exp` `1-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `inv-pow`

Counts

4 → 155

Calls

4 calls:

2.0ms	(- a (* (/ b a) b))
1.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
7.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
8.0ms	(* (/ b a) b)

series125.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- a (* (/ b a) b))
15.0ms	(sqrt (fabs (/ 1 (/ a (- a (* (/ b a) b))))))
53.0ms	(/ 1 (/ a (- a (* (/ b a) b))))
23.0ms	(* (/ b a) b)

simplify1.9s

Counts

167 → 167

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	255	2725
1	556	2426
2	1344	2149
done	5000	2080

prune350.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (exp (log1p (* (/ b a) (- (/ b a)))))))
0.0b	(log1p (* (/ b a) (- (/ b a))))
0.4b	(* (/ b a) (- (/ b a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u`
3×	`sqrt-prod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`prod-exp` `cbrt-unprod` `distribute-neg-frac` `unswap-sqr`
1×	`cbrt-undiv` `frac-times` `neg-mul-1` `rem-sqrt-square` `log1p-udef` `sqrt-pow1` `pow1/2` `log1p-expm1` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `*-commutative` `distribute-rgt-neg-out`

Counts

3 → 90

Calls

3 calls:

1.0ms	(sqrt (fabs (exp (log1p (* (/ b a) (- (/ b a)))))))
0.0ms	(log1p (* (/ b a) (- (/ b a))))
22.0ms	(* (/ b a) (- (/ b a)))

series123.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(sqrt (fabs (exp (log1p (* (/ b a) (- (/ b a)))))))
65.0ms	(log1p (* (/ b a) (- (/ b a))))
40.0ms	(* (/ b a) (- (/ b a)))

simplify913.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (381.0ms)

Iter	Nodes	Cost
0	173	1137
1	442	1056
2	1764	981
done	5000	981

prune311.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

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	9	12
1	14	12
done	14	12

end0.0ms

sample608.0ms

Algorithm

intervals

Results

190.0ms	8000×	body	80	valid
100.0ms	8000×	pre	80	true
94.0ms	8109×	pre	80	false