Details

analyze9.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 99.996948%

sample17.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify15.0ms

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

prune3.0ms

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: 32.6b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

4.7b	(- (* x x) (* (* y 4.0) y))
31.9b	(/ (- (* 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)))

series20.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify180.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (25.0ms)

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

prune85.0ms

Filtered

39 candidates to 50 candidates (-28.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Merged error: 0.4b

Counts

51 → 5

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Merged error: 0.4b

Counts

5 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
22.5b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
24.6b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-/r/`
7×	`add-cube-cbrt` `times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv`
3×	`pow1` `distribute-rgt-out--`
2×	`frac-2neg` `clear-num` `associate-/l*` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

3 → 68

Calls

3 calls:

14.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
8.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
6.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series33.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
9.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
8.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	362	890
1	1737	796
2	5001	796

prune92.0ms

Filtered

55 candidates to 77 candidates (-40.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Merged error: 0.4b

Counts

82 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

18.4b	(* (/ 1 (* (cbrt (+ (* x x) (* (* y 4.0) y))) (cbrt (+ (* x x) (* (* y 4.0) y))))) (/ (- (* x x) (* (* y 4.0) y)) (cbrt (+ (* x x) (* (* y 4.0) y)))))
31.6b	(cbrt (+ (* x x) (* (* y 4.0) y)))
31.6b	(cbrt (+ (* x x) (* (* y 4.0) y)))
31.6b	(cbrt (+ (* x x) (* (* y 4.0) y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

28.0ms	(* (/ 1 (* (cbrt (+ (* x x) (* (* y 4.0) y))) (cbrt (+ (* x x) (* (* y 4.0) y))))) (/ (- (* x x) (* (* y 4.0) y)) (cbrt (+ (* x x) (* (* y 4.0) y)))))
3.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
3.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
3.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (/ 1 (* (cbrt (+ (* x x) (* (* y 4.0) y))) (cbrt (+ (* x x) (* (* y 4.0) y))))) (/ (- (* x x) (* (* y 4.0) y)) (cbrt (+ (* x x) (* (* y 4.0) y)))))
22.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
25.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
22.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))

simplify81.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	623	2733
1	2850	2369
2	5001	2162

prune291.0ms

Filtered

92 candidates to 131 candidates (-42.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	131	5	136

Merged error: 0.4b

Counts

136 → 5

Details

analyze9.0ms

sample17.0ms

simplify15.0ms

prune3.0ms

localize7.0ms

rewrite12.0ms

series20.0ms

simplify180.0ms

prune85.0ms

localize1.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune8.0ms

localize11.0ms

rewrite31.0ms

series33.0ms

simplify45.0ms

prune92.0ms

localize15.0ms

rewrite43.0ms

series82.0ms

simplify81.0ms

prune291.0ms

regimes261.0ms

bsearch0.0ms

Profiling