Details

sample34.0ms

Algorithm

intervals

Results

18.0ms

511×

body

valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	50	6
2	159	6
3	351	6
4	609	6
5	733	6
6	1068	6
7	1342	6
8	1506	6
9	1553	6
10	1553	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

7.0ms	(- (* z z) t)
4.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
9.0ms	(* (* y 4.0) (- (* z z) t))

series161.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(- (* z z) t)
78.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
62.0ms	(* (* y 4.0) (- (* z z) t))

simplify43.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	292	385
1	1348	342
2	5001	337

prune143.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
2.4b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
5.7b	(* (* y 4.0) (- (* z z) t))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sqrt-div` `associate-*r/` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

3.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
3.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
9.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))

series418.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
138.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
67.0ms	(* (* y 4.0) (- (* z z) t))
66.0ms	(* (* y 4.0) (- (* z z) t))

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	270	654
1	1170	602
2	5002	598

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* y 4.0) (- (* z z) t))
6.3b	(cbrt (- (* z z) t))
6.3b	(cbrt (- (* z z) t))
6.3b	(cbrt (- (* z z) t))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`flip3--` `associate-r` `flip--` `add-log-exp` `difference-of-squares`
3×	`pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`associate-l` `*-commutative`

Counts

4 → 67

Calls

4 calls:

8.0ms	(* (* y 4.0) (- (* z z) t))
4.0ms	(cbrt (- (* z z) t))
4.0ms	(cbrt (- (* z z) t))
8.0ms	(cbrt (- (* z z) t))

series346.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* y 4.0) (- (* z z) t))
94.0ms	(cbrt (- (* z z) t))
94.0ms	(cbrt (- (* z z) t))
94.0ms	(cbrt (- (* z z) t))

simplify42.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	501
1	1086	451
2	5001	444

prune343.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.7b	(sqrt (- (* z z) t))
5.7b	(sqrt (- (* z z) t))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 89

Calls

4 calls:

10.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
16.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
4.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series244.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
68.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
48.0ms	(sqrt (- (* z z) t))
54.0ms	(sqrt (- (* z z) t))

simplify54.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	372	771
1	1753	649
2	5001	641

prune263.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.7b

regimes390.0ms

Accuracy

85.7% (0.5b remaining)

Error of 3.1b against oracle of 2.6b and baseline of 5.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample968.0ms

Algorithm

intervals

Results

568.0ms

15913×

body

valid