Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	309×	body	80	nan
8.0ms	316×	body	80	valid

simplify121.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	39	5
3	71	5
4	167	5
5	298	5
6	545	5
7	2142	5
8	5001	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 23.4b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (sqrt (- (* y y) (* z z))))
1.8b	(- (* y y) (* z z))
22.5b	(sqrt (- (* y y) (* z z)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

379×	`add-sqr-sqrt`
225×	`prod-diff`
198×	`*-un-lft-identity`
162×	`add-cube-cbrt`
129×	`swap-sqr` `associate-r`
108×	`associate-l`
75×	`difference-of-squares`
67×	`sqrt-prod`
63×	`unswap-sqr`
62×	`*-commutative`
15×	`fma-neg` `distribute-lft-out--`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div`
3×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`associate-*r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

3 → 387

Calls

3 calls:

27.0ms	(* x (sqrt (- (* y y) (* z z))))
28.0ms	(- (* y y) (* z z))
34.0ms	(sqrt (- (* y y) (* z z)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(* x (sqrt (- (* y y) (* z z))))
36.0ms	(- (* y y) (* z z))
64.0ms	(sqrt (- (* y y) (* z z)))

simplify118.0ms

Algorithm

egg-herbie

Counts

396 → 396

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	735	3922
1	2024	2710
2	5001	2176

prune305.0ms

Filtered

396 candidates to 81 candidates (20.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	392	4	396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	393	4	397

Merged error: 0.3b

Counts

397 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* y y) (* z z))
1.8b	(- (* y y) (* z z))
23.3b	(cbrt (- (* y y) (* z z)))
23.3b	(cbrt (- (* y y) (* z z)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

640×	`add-sqr-sqrt`
450×	`prod-diff`
364×	`*-un-lft-identity`
316×	`add-cube-cbrt`
234×	`swap-sqr`
202×	`associate-l`
186×	`associate-r`
102×	`*-commutative` `unswap-sqr`
100×	`difference-of-squares`
66×	`cbrt-prod`
30×	`fma-neg`
20×	`distribute-lft-out--`
8×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `pow1/3` `diff-log`

Counts

4 → 658

Calls

4 calls:

28.0ms	(- (* y y) (* z z))
25.0ms	(- (* y y) (* z z))
18.0ms	(cbrt (- (* y y) (* z z)))
19.0ms	(cbrt (- (* y y) (* z z)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* y y) (* z z))
36.0ms	(- (* y y) (* z z))
137.0ms	(cbrt (- (* y y) (* z z)))
144.0ms	(cbrt (- (* y y) (* z z)))

simplify146.0ms

Algorithm

egg-herbie

Counts

670 → 670

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	685	7364
1	1752	4948
2	5001	3862

prune429.0ms

Filtered

670 candidates to 102 candidates (15.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	670	0	670
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	670	4	674

Merged error: 0.3b

Counts

674 → 4

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 0.3b

Counts

4 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- y z))
0.0b	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.0b	(sqrt (+ y z))
0.3b	(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`associate-r`
39×	`sqrt-prod`
28×	`*-un-lft-identity` `sqrt-div`
17×	`associate-l` `unswap-sqr`
16×	`add-cube-cbrt`
15×	`pow1`
12×	`associate-*r/`
11×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `associate-*l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
2×	`rem-sqrt-square`
1×	`sqrt-unprod` `hypot-def`

Counts

4 → 137

Calls

4 calls:

4.0ms	(sqrt (- y z))
20.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
4.0ms	(sqrt (+ y z))
15.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (- y z))
106.0ms	(* x (* (sqrt (+ y z)) (sqrt (- y z))))
39.0ms	(sqrt (+ y z))
77.0ms	(* (sqrt (+ y z)) (sqrt (- y z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	421	988
1	1707	942
2	5001	917

prune414.0ms

Filtered

149 candidates to 102 candidates (68.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	149	4	153

Merged error: 0.3b

Counts

153 → 4

Details

sample36.0ms

simplify121.0ms

prune3.0ms

localize8.0ms

rewrite115.0ms

series194.0ms

simplify118.0ms

prune305.0ms

localize17.0ms

rewrite136.0ms

series364.0ms

simplify146.0ms

prune429.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune4.0ms

localize9.0ms

rewrite49.0ms

series308.0ms

simplify72.0ms

prune414.0ms

regimes260.0ms

bsearch15.0ms