Details

sample25.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

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: 4.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

9.0ms	(+ (+ alpha beta) (* beta alpha))
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ alpha beta) (* beta alpha))
135.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune842.0ms

Filtered

475 candidates to 280 candidates (58.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	466	9	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	467	9	476

Merged error: 0.7b

Counts

476 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.2b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

65×	`times-frac`
57×	`*-un-lft-identity`
50×	`add-exp-log`
41×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
32×	`add-cbrt-cube`
22×	`div-exp`
16×	`associate-/r/`
15×	`associate-r`
13×	`cbrt-undiv` `flip3-+` `flip-+`
12×	`prod-exp`
11×	`distribute-lft-out`
10×	`associate-/l*`
9×	`add-log-exp`
8×	`div-inv`
7×	`associate-/r*` `associate-/l/`
6×	`pow1` `cbrt-unprod`
4×	`frac-times` `associate-l` `associate-*l/`
3×	`rec-exp` `1-exp` `sum-log` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv`
1×	`+-commutative` `associate-+l+` `pow-prod-down` `*-commutative`

Counts

4 → 161

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
25.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
27.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
135.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
74.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

simplify133.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	856	3084
1	4896	2762
2	5001	2762

prune342.0ms

Filtered

173 candidates to 118 candidates (68.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	173	9	182

Merged error: 0.7b

Counts

182 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

17.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series392.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
103.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394

prune366.0ms

Filtered

171 candidates to 99 candidates (57.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	171	9	180

Merged error: 0.7b

Counts

180 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
46×	`times-frac`
45×	`sqrt-prod`
38×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `distribute-lft-out`
8×	`pow1`
7×	`flip3-+` `associate-l` `flip-+` `associate-/l*`
6×	`unswap-sqr`
4×	`associate-/r/` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 137

Calls

4 calls:

16.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
25.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series351.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
74.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	503	2153
1	2064	1923
2	5003	1855

prune295.0ms

Filtered

149 candidates to 96 candidates (64.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	149	9	158

Merged error: 0.7b

Counts

158 → 9

Details

sample25.0ms

simplify82.0ms

prune2.0ms

localize15.0ms

rewrite108.0ms

series372.0ms

simplify139.0ms

prune842.0ms

localize14.0ms

rewrite81.0ms

series367.0ms

simplify133.0ms

prune342.0ms

localize20.0ms

rewrite51.0ms

series392.0ms

simplify68.0ms

prune366.0ms

localize15.0ms

rewrite61.0ms

series351.0ms

simplify68.0ms

prune295.0ms

regimes103.0ms

bsearch5.0ms

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