Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify84.0ms

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: 3.6b

Counts

2 → 1

localize12.0ms

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

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:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
41.0ms	(/ (/ (/ (+ (+ (+ 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))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
138.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms	(/ (/ (/ (+ (+ (+ 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))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune866.0ms

Filtered

475 candidates to 280 candidates (58.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	468	7	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	469	7	476

Merged error: 1.1b

Counts

476 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(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:

27.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (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))

series362.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
194.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (49.0ms)

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

prune328.0ms

Filtered

149 candidates to 98 candidates (65.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Merged error: 1.1b

Counts

156 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.4b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-div`
36×	`flip3-+` `flip-+`
32×	`frac-times`
26×	`associate-/r/`
25×	`add-exp-log`
18×	`sqrt-div`
16×	`associate-*r/`
15×	`add-cbrt-cube`
13×	`*-un-lft-identity`
12×	`cbrt-prod`
10×	`associate-*l/`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/l/`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 101

Calls

4 calls:

9.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
42.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
490.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	849	2686
1	3123	2411
2	5001	2386

prune502.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	112	8	120

Merged error: 1.1b

Counts

120 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.3b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
216×	`*-un-lft-identity`
161×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
78×	`associate-l`
38×	`distribute-lft-out`
37×	`difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r/`
25×	`associate-/l*`
18×	`associate-r`
14×	`cbrt-undiv` `div-exp` `div-inv`
13×	`flip3-+` `flip-+`
11×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`frac-times` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 308

Calls

4 calls:

59.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
31.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
43.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
163.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1417	7781
1	5001	7281

prune788.0ms

Filtered

320 candidates to 239 candidates (74.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	320	8	328

Merged error: 1.1b

Counts

328 → 8

Details

sample28.0ms

simplify84.0ms

prune2.0ms

localize12.0ms

rewrite115.0ms

series377.0ms

simplify140.0ms

prune866.0ms

localize18.0ms

rewrite61.0ms

series362.0ms

simplify73.0ms

prune328.0ms

localize21.0ms

rewrite71.0ms

series679.0ms

simplify92.0ms

prune502.0ms

localize17.0ms

rewrite137.0ms

series510.0ms

simplify94.0ms

prune788.0ms

regimes85.0ms

bsearch4.0ms

Profiling