Details

sample34.0ms

Algorithm

intervals

Results

18.0ms

481×

body

valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 4.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
4.6b	(* (* 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:

3.0ms	(- (* z z) t)
3.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
13.0ms	(* (* y 4.0) (- (* z z) t))

series161.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(- (* z z) t)
77.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
63.0ms	(* (* 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

prune147.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (* 1 (- (* z z) t))))
4.6b	(* (* y 4.0) (* 1 (- (* z z) t)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

3.0ms	(- (* z z) t)
4.0ms	(- (* x x) (* (* y 4.0) (* 1 (- (* z z) t))))
19.0ms	(* (* y 4.0) (* 1 (- (* z z) t)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(- (* z z) t)
75.0ms	(- (* x x) (* (* y 4.0) (* 1 (- (* z z) t))))
64.0ms	(* (* y 4.0) (* 1 (- (* z z) t)))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	375	505
1	1603	429
2	5002	422

prune140.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

localize11.0ms

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)))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))

rewrite79.0ms

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:

14.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
54.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
4.0ms	(sqrt (- (* z z) t))
4.0ms	(sqrt (- (* z z) t))

series217.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
62.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
48.0ms	(sqrt (- (* z z) t))
43.0ms	(sqrt (- (* z z) t))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	372	769
1	1759	649
2	5001	641

prune272.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-div`
23×	`sqrt-prod`
17×	`add-sqr-sqrt`
16×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`flip3--` `flip--`
8×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-*l/`
1×	`associate-l` `*-commutative`

Counts

4 → 84

Calls

4 calls:

47.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
4.0ms	(sqrt (- (* z z) t))
4.0ms	(sqrt (- (* z z) t))
4.0ms	(sqrt (- (* z z) t))

series237.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
49.0ms	(sqrt (- (* z z) t))
44.0ms	(sqrt (- (* z z) t))
49.0ms	(sqrt (- (* z z) t))

simplify51.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	380	822
1	1670	755
2	5001	718

prune329.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.7b

regimes517.0ms

Accuracy

80% (0.7b remaining)

Error of 3.3b against oracle of 2.6b and baseline of 6.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	32	17
2	32	17

end0.0ms

sample901.0ms

Algorithm

intervals

Results

509.0ms

15894×

body

valid