Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	292×	pre	80	false

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	47	7
2	106	7
3	265	7
4	1495	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b	(- (* a a) (* b b))
14.8b	(/ (- (* a a) (* b b)) (* a a))

rewrite13.0ms

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×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 52

Calls

3 calls:

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

series99.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
30.0ms	(- (* a a) (* b b))
52.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify160.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	228	418
1	970	368
2	4781	367
3	5001	366

prune131.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

8.0ms	(/ (+ a b) a)
1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
32.0ms	(* (/ (+ a b) a) (/ (- a b) a))
8.0ms	(/ (- a b) a)

series129.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ a b) a)
16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
61.0ms	(* (/ (+ a b) a) (/ (- a b) a))
30.0ms	(/ (- a b) a)

simplify62.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5001	867

prune319.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
34×	`times-frac`
27×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
7×	`pow1` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`frac-times` `flip3-+` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 122

Calls

4 calls:

1.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
10.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
25.0ms	(* (+ a b) (/ (- a b) a))
8.0ms	(/ (- a b) a)

series167.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
61.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
60.0ms	(* (+ a b) (/ (- a b) a))
30.0ms	(/ (- a b) a)

simplify65.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	440	815
1	2436	731
2	5001	729

prune285.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

end0.0ms

sample595.0ms

Algorithm

intervals

Results

197.0ms	8000×	body	80	valid
91.0ms	8107×	pre	80	false
89.0ms	8000×	pre	80	true