Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	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: 37.9b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-/r` `sum-log` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

3 → 67

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series260.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
168.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	259	759
1	1001	695
2	4255	689
3	5001	687

prune190.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	5	77

Merged error: 18.4b

Counts

77 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`associate-*r/`
3×	`flip3-+` `associate-r` `associate-l` `sum-log` `flip-+`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 48

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
56.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
169.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify37.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	244	469
1	1256	426
2	5002	424

prune110.0ms

Filtered

57 candidates to 39 candidates (68.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Merged error: 18.4b

Counts

62 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.2b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `sum-log` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 91

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series365.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
228.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify122.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	264	1246
1	989	1175
2	4693	1148
3	5002	1148

prune185.0ms

Filtered

100 candidates to 62 candidates (62.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 18.3b

Counts

105 → 8

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

5.0ms

(* x (sqrt 0.3333333333333333))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(* x (sqrt 0.3333333333333333))

simplify57.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	69	84
1	245	80
2	569	78
3	893	78
4	2001	78
5	5001	78

prune32.0ms

Filtered

25 candidates to 14 candidates (56.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	20	13	33

Merged error: 18.3b

Counts

33 → 13

Details

sample20.0ms

simplify6.0ms

prune2.0ms

localize12.0ms

rewrite21.0ms

series260.0ms

simplify121.0ms

prune190.0ms

localize9.0ms

rewrite20.0ms

series262.0ms

simplify37.0ms

prune110.0ms

localize10.0ms

rewrite22.0ms

series365.0ms

simplify122.0ms

prune185.0ms

localize7.0ms

rewrite5.0ms

series40.0ms

simplify57.0ms

prune32.0ms

regimes459.0ms

bsearch2.0ms

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