Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify7.0ms

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: 37.7b

Counts

2 → 1

localize9.0ms

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)
35.0b	(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))

series246.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
52.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
159.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify115.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	259	758
1	1001	695
2	4255	689
3	5001	687

prune183.0ms

Filtered

76 candidates to 60 candidates (78.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 19.0b

Counts

77 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `add-log-exp` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 77

Calls

3 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
14.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
170.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
98.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	288	917
1	1133	879
2	5002	855

prune178.0ms

Filtered

86 candidates to 57 candidates (66.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 19.0b

Counts

92 → 6

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))
34.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite23.0ms

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)))

series353.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
222.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify119.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (27.0ms)

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

prune179.0ms

Filtered

100 candidates to 61 candidates (61.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	97	9	106

Merged error: 18.9b

Counts

106 → 9

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite9.0ms

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))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(* 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

prune33.0ms

Filtered

25 candidates to 14 candidates (56.0%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	22	12	34

Merged error: 18.9b

Counts

34 → 12

Details

sample24.0ms

simplify7.0ms

prune2.0ms

localize9.0ms

rewrite21.0ms

series246.0ms

simplify115.0ms

prune183.0ms

localize11.0ms

rewrite31.0ms

series305.0ms

simplify41.0ms

prune178.0ms

localize10.0ms

rewrite23.0ms

series353.0ms

simplify119.0ms

prune179.0ms

localize4.0ms

rewrite9.0ms

series38.0ms

simplify57.0ms

prune33.0ms

regimes530.0ms

bsearch3.0ms

Profiling