Details

sample34.0ms

Algorithm

intervals

Results

18.0ms

510×

body

valid

simplify85.0ms

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: 6.6b

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)))
6.2b	(* (* y 4.0) (- (* z z) t))

rewrite23.0ms

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)))
15.0ms	(* (* y 4.0) (- (* z z) t))

series161.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(- (* z z) t)
75.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
64.0ms	(* (* y 4.0) (- (* z z) t))

simplify44.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (38.0ms)

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

prune137.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
6.8b	(cbrt (- (* z z) t))
6.8b	(cbrt (- (* z z) t))
6.8b	(cbrt (- (* z z) t))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

38.0ms	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
3.0ms	(cbrt (- (* z z) t))
3.0ms	(cbrt (- (* z z) t))
3.0ms	(cbrt (- (* z z) t))

series370.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* y 4.0) (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))))
93.0ms	(cbrt (- (* z z) t))
89.0ms	(cbrt (- (* z z) t))
90.0ms	(cbrt (- (* z z) t))

simplify120.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	315	709
1	1057	625
2	4510	613
3	5001	613

prune289.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

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)))
6.2b	(sqrt (- (* z z) t))
6.2b	(sqrt (- (* z z) t))

rewrite77.0ms

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:

16.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
49.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series224.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
62.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
44.0ms	(sqrt (- (* z z) t))
48.0ms	(sqrt (- (* z z) t))

simplify57.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (49.0ms)

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

prune270.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
6.2b	(sqrt (- (* z z) t))
6.2b	(sqrt (- (* z z) t))
6.2b	(sqrt (- (* z z) t))

rewrite71.0ms

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:

50.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))
9.0ms	(sqrt (- (* z z) t))

series258.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
50.0ms	(sqrt (- (* z z) t))
45.0ms	(sqrt (- (* z z) t))
60.0ms	(sqrt (- (* z z) t))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

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

prune337.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.9b

regimes405.0ms

Accuracy

85.5% (0.5b remaining)

Error of 3.4b against oracle of 2.9b and baseline of 6.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample883.0ms

Algorithm

intervals

Results

491.0ms

15956×

body

valid