Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	272×	body	80	valid
12.0ms	272×	body	80	nan

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	21	5
1	51	4
2	86	4
3	126	4
4	151	4
5	169	4
6	185	4
7	187	4
8	187	4

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* y (sqrt z)))
0.3b	(* y (sqrt z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

2.0ms	(+ x (* y (sqrt z)))
5.0ms	(* y (sqrt z))

series75.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ x (* y (sqrt z)))
40.0ms	(* y (sqrt z))

simplify126.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	231	204
1	879	180
2	4188	173
3	5001	170

prune130.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt z))
0.1b	(sqrt (sqrt z))
0.2b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`

Counts

4 → 96

Calls

4 calls:

1.0ms	(sqrt (sqrt z))
1.0ms	(sqrt (sqrt z))
7.0ms	(* y (sqrt (sqrt z)))
16.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (sqrt z))
136.0ms	(sqrt (sqrt z))
83.0ms	(* y (sqrt (sqrt z)))
44.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	351	549
1	1510	488
2	5001	461

prune285.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (* (pow z 1/4) y) (sqrt (sqrt z))))
0.1b	(sqrt (sqrt z))
0.2b	(* (pow z 1/4) y)
0.3b	(* (* (pow z 1/4) y) (sqrt (sqrt z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-exp-log` `sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`pow1` `associate-l`
6×	`add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `sqrt-pow1` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `pow1/2` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `flip-+`

Counts

4 → 91

Calls

4 calls:

2.0ms	(+ x (* (* (pow z 1/4) y) (sqrt (sqrt z))))
1.0ms	(sqrt (sqrt z))
5.0ms	(* (pow z 1/4) y)
12.0ms	(* (* (pow z 1/4) y) (sqrt (sqrt z)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ x (* (* (pow z 1/4) y) (sqrt (sqrt z))))
144.0ms	(sqrt (sqrt z))
96.0ms	(* (pow z 1/4) y)
126.0ms	(* (* (pow z 1/4) y) (sqrt (sqrt z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	493	603
1	2012	550
2	5001	538

prune333.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 z) -1/4)
0.1b	(sqrt (sqrt z))
0.2b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
34×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `unpow-prod-down` `-un-lft-identity` `associate-r*`
22×	`sqrt-prod`
19×	`prod-exp`
18×	`times-frac`
12×	`pow-exp`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`div-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `unswap-sqr`
2×	`rem-sqrt-square` `pow1/2` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 125

Calls

4 calls:

4.0ms	(pow (/ 1 z) -1/4)
1.0ms	(sqrt (sqrt z))
9.0ms	(* y (sqrt (sqrt z)))
22.0ms	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

series503.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(pow (/ 1 z) -1/4)
141.0ms	(sqrt (sqrt z))
85.0ms	(* y (sqrt (sqrt z)))
87.0ms	(* (* y (sqrt (sqrt z))) (pow (/ 1 z) -1/4))

simplify78.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	641	805
1	2903	730
2	5003	713

prune364.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes286.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample823.0ms

Algorithm

intervals

Results

249.0ms	8546×	body	80	valid
231.0ms	8377×	body	80	nan