Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1343	7
7	5001	7

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: 24.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
23.8b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
8.0ms	(* (- x y) (+ x y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
39.0ms	(* (- x y) (+ x y))
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	419	577
1	2448	504
2	5003	497

prune153.0ms

Filtered

82 candidates to 62 candidates (75.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.3b

Counts

83 → 4

localize0.0ms

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

prune4.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.3b

Counts

4 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) x)
0.0b	(* (- x y) y)
23.8b	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
12×	`times-frac` `associate-*l/`
10×	`add-exp-log` `associate-l` `add-cbrt-cube`
8×	`pow1`
6×	`flip3--` `associate-r` `flip--` `associate-/l/` `add-log-exp`
4×	`frac-add` `distribute-lft-out` `associate-/l*`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
9.0ms	(* (- x y) x)
6.0ms	(* (- x y) y)
12.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
34.0ms	(* (- x y) x)
38.0ms	(* (- x y) y)
49.0ms	(/ (+ (* (- x y) x) (* (- x y) y)) (+ (* x x) (* y y)))

simplify59.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	418	798
1	2016	705
2	5001	699

prune187.0ms

Filtered

106 candidates to 79 candidates (74.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	106	4	110

Merged error: 0.3b

Counts

110 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x y) (+ x y))
22.7b	(sqrt (+ (* x x) (* y y)))
22.7b	(sqrt (+ (* x x) (* y y)))
22.8b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`add-cube-cbrt` `sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`pow1` `frac-times` `associate-/l/`
6×	`flip3--` `times-frac` `sqrt-div` `associate-/r*` `flip--`
5×	`associate-l`
4×	`associate-r/` `associate-r` `associate-l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

8.0ms	(* (- x y) (+ x y))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
17.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (- x y) (+ x y))
34.0ms	(sqrt (+ (* x x) (* y y)))
34.0ms	(sqrt (+ (* x x) (* y y)))
81.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify63.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	429	796
1	2316	732
2	5001	725

prune218.0ms

Filtered

110 candidates to 84 candidates (76.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Merged error: 0.3b

Counts

114 → 4

Details

sample26.0ms

simplify63.0ms

prune2.0ms

localize8.0ms

rewrite26.0ms

series128.0ms

simplify67.0ms

prune153.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune4.0ms

localize9.0ms

rewrite35.0ms

series146.0ms

simplify59.0ms

prune187.0ms

localize11.0ms

rewrite35.0ms

series193.0ms

simplify63.0ms

prune218.0ms

regimes74.0ms

bsearch2.0ms

Profiling