Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	9
1	36	9
2	68	9
3	117	9
4	174	9
5	195	9
6	197	9
7	197	9

prune2.0ms

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: 30.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

4.3b	(- (* x x) (* (* y 4.0) y))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series103.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* x x) (* (* y 4.0) y))
60.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify185.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	221	583
1	964	535
2	4800	534
3	5002	534

prune97.0ms

Filtered

50 candidates to 39 candidates (78.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	5	51

Merged error: 0.1b

Counts

51 → 5

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify4.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Merged error: 0.1b

Counts

5 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
0.0b	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
4.3b	(- (* x x) (* (* y 4.0) y))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`exp-prod`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
16×	`log-pow`
7×	`add-log-exp`
6×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`pow1`
3×	`log-prod` `flip3-+` `div-sub` `associate-/r` `flip-+` `div-inv` `associate-/l`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 96

Calls

4 calls:

7.0ms	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
8.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
63.0ms	(log (exp (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
39.0ms	(- (* x x) (* (* y 4.0) y))
62.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	281	1237
1	1067	1137
2	5001	1134

prune238.0ms

Filtered

108 candidates to 85 candidates (78.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	108	5	113

Merged error: 0.1b

Counts

113 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
0.0b	(pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
4.3b	(- (* x x) (* (* y 4.0) y))
29.5b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`pow-unpow`
9×	`add-exp-log`
7×	`log-prod`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`rem-log-exp` `pow-exp` `associate-/r/`
3×	`div-sub` `associate-/r` `associate-/l`
2×	`pow-to-exp` `e-exp-1` `flip3--` `flip3-+` `flip--` `flip-+` `div-inv` `associate-/l/` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `sub-neg` `log-div` `pow-pow` `frac-2neg` `diff-log` `div-exp` `clear-num` `log-pow`

Counts

4 → 95

Calls

4 calls:

2.0ms	(log (pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
7.0ms	(pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
3.0ms	(- (* x x) (* (* y 4.0) y))
12.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(log (pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
102.0ms	(pow E (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
45.0ms	(- (* x x) (* (* y 4.0) y))
59.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify58.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	365	1255
1	1573	1160
2	5001	1155

prune231.0ms

Filtered

107 candidates to 79 candidates (73.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0.1b

Counts

112 → 5

Details

sample16.0ms

simplify17.0ms

prune2.0ms

localize10.0ms

rewrite12.0ms

series103.0ms

simplify185.0ms

prune97.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify4.0ms

prune7.0ms

localize11.0ms

rewrite29.0ms

series244.0ms

simplify43.0ms

prune238.0ms

localize12.0ms

rewrite26.0ms

series332.0ms

simplify58.0ms

prune231.0ms

regimes160.0ms

bsearch3.0ms

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