Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	88×	body	1280	valid
5.0ms	50×	body	640	valid
3.0ms	23×	body	2560	valid
2.0ms	69×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	8×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	5
1	43	5
2	91	5
3	194	5
4	321	5
5	579	5
6	1088	5
7	1305	5
8	1305	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x y) z)
11.1b	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
7×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `sum-log`
3×	`diff-log`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

2 → 29

Calls

2 calls:

3.0ms	(+ (* x y) z)
23.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(+ (* x y) z)
37.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	178	220
1	602	204
2	2697	203
3	5001	203

prune84.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 44.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x y) (* x y))
5.8b	(- (* (* x y) (* x y)) (* z z))
12.8b	(- (fma x y z) (+ 1.0 (/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))))
33.7b	(/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
18×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
17×	`pow-prod-down`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
11×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
6×	`difference-of-squares`
4×	`flip3--` `pow-sqr` `pow-prod-up` `flip--` `associate-/l*`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `pow-plus` `div-sub` `associate-/r/` `associate-/l/` `distribute-lft-out--`
1×	`cbrt-undiv` `pow2` `associate-+r-` `frac-2neg` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv` `distribute-lft-out` `associate--r+` `associate--r-`

Counts

4 → 101

Calls

4 calls:

10.0ms	(* (* x y) (* x y))
11.0ms	(- (* (* x y) (* x y)) (* z z))
112.0ms	(- (fma x y z) (+ 1.0 (/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))))
36.0ms	(/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))

series216.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x y) (* x y))
56.0ms	(- (* (* x y) (* x y)) (* z z))
71.0ms	(- (fma x y z) (+ 1.0 (/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))))
53.0ms	(/ (- (* (* x y) (* x y)) (* z z)) (- (* x y) z))

simplify63.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	427	979
1	2002	820
2	5001	784

prune276.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 44.3b

localize20.0ms

Local error

Found 4 expressions with local error:

33.4b	(cbrt (* (* x y) (* x y)))
33.4b	(cbrt (* (* x y) (* x y)))
33.4b	(cbrt (* (* x y) (* x y)))
33.7b	(/ (- (* (* (cbrt (* (* x y) (* x y))) (cbrt (* (* x y) (* x y)))) (cbrt (* (* x y) (* x y)))) (* z z)) (- (* x y) z))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-/r` `associate-/l`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

11.0ms	(cbrt (* (* x y) (* x y)))
9.0ms	(cbrt (* (* x y) (* x y)))
9.0ms	(cbrt (* (* x y) (* x y)))
62.0ms	(/ (- (* (* (cbrt (* (* x y) (* x y))) (cbrt (* (* x y) (* x y)))) (cbrt (* (* x y) (* x y)))) (* z z)) (- (* x y) z))

series316.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (* (* x y) (* x y)))
89.0ms	(cbrt (* (* x y) (* x y)))
87.0ms	(cbrt (* (* x y) (* x y)))
51.0ms	(/ (- (* (* (cbrt (* (* x y) (* x y))) (cbrt (* (* x y) (* x y)))) (cbrt (* (* x y) (* x y)))) (* z z)) (- (* x y) z))

simplify95.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	287	1192
1	941	1061
2	3271	900
3	5001	863

prune304.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 44.3b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(+ (- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z)))) (/ (* z z) (- (* x y) z)))
12.0b	(- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z))))
20.9b	(/ (* (* x y) (* x y)) (- (* x y) z))
24.7b	(/ (* z z) (- (* x y) z))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
22×	`*-un-lft-identity`
18×	`add-log-exp`
10×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt`
7×	`cbrt-undiv` `div-exp`
6×	`times-frac` `associate-/r*`
5×	`sum-log` `distribute-lft-out`
4×	`pow1` `flip3--` `diff-log` `associate-/r/` `flip--` `distribute-lft-out--`
2×	`sub-neg` `associate-+l+` `frac-2neg` `frac-add` `clear-num` `div-inv` `associate-/l*`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `associate--r+` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

241.0ms	(+ (- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z)))) (/ (* z z) (- (* x y) z)))
37.0ms	(- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z))))
16.0ms	(/ (* (* x y) (* x y)) (- (* x y) z))
7.0ms	(/ (* z z) (- (* x y) z))

series217.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z)))) (/ (* z z) (- (* x y) z)))
56.0ms	(- (fma x y z) (+ 1.0 (/ (* (* x y) (* x y)) (- (* x y) z))))
37.0ms	(/ (* (* x y) (* x y)) (- (* x y) z))
57.0ms	(/ (* z z) (- (* x y) z))

simplify69.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	517	1148
1	2723	1043
2	5002	1043

prune237.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 44.2b

regimes262.0ms

Accuracy

0% (1.3b remaining)

Error of 46.1b against oracle of 44.8b and baseline of 46.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample878.0ms

Algorithm

intervals

Results

335.0ms	2668×	body	1280	valid
166.0ms	1654×	body	640	valid
88.0ms	595×	body	2560	valid
53.0ms	2034×	body	80	valid
52.0ms	714×	body	320	valid
17.0ms	335×	body	160	valid