Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

264×

body

valid

simplify153.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
1.0b	(+ (* x y) (* z (- t a)))
23.8b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

7.0ms	(* z (- t a))
8.0ms	(* z (- b y))
7.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* z (- t a))
37.0ms	(* z (- b y))
47.0ms	(+ (* x y) (* z (- t a)))
338.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify99.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune429.0ms

Filtered

173 candidates to 100 candidates (57.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	162	11	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 23.9b

Counts

174 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(fma x y (* t z))
1.6b	(+ (fma x y (* t z)) (* z (- a)))
23.8b	(/ (+ (fma x y (* t z)) (* z (- a))) (+ y (* z (- b y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `distribute-rgt-neg-out` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `associate-/r` `flip-+` `associate-/l`
2×	`sub-neg` `div-sub` `associate-*r/` `unsub-neg` `associate-/r/` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

7.0ms	(* z (- b y))
1.0ms	(fma x y (* t z))
3.0ms	(+ (fma x y (* t z)) (* z (- a)))
7.0ms	(/ (+ (fma x y (* t z)) (* z (- a))) (+ y (* z (- b y))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* z (- b y))
45.0ms	(fma x y (* t z))
46.0ms	(+ (fma x y (* t z)) (* z (- a)))
321.0ms	(/ (+ (fma x y (* t z)) (* z (- a))) (+ y (* z (- b y))))

simplify78.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	414	1024
1	1888	819
2	5001	807

prune332.0ms

Filtered

122 candidates to 82 candidates (67.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Merged error: 21.6b

Counts

133 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma t z (* x y))
2.1b	(/ a (/ (fma z (- b y) y) z))
13.0b	(/ (fma z (- b y) y) z)
20.8b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma t z (* x y))
6.0ms	(/ a (/ (fma z (- b y) y) z))
7.0ms	(/ (fma z (- b y) y) z)
4.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series294.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma t z (* x y))
63.0ms	(/ a (/ (fma z (- b y) y) z))
42.0ms	(/ (fma z (- b y) y) z)
144.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify72.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	430	1181
1	1684	1108
2	5001	1107

prune508.0ms

Filtered

152 candidates to 124 candidates (81.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	152	10	162

Merged error: 12.4b

Counts

162 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
0.5b	(fma t z (* x y))
2.1b	(/ a (- (+ (/ y z) b) y))
20.8b	(/ (fma t z (* x y)) (fma z (- b y) y))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

560×	`*-un-lft-identity`
496×	`times-frac`
426×	`add-sqr-sqrt`
328×	`add-cube-cbrt`
312×	`prod-diff`
92×	`distribute-lft-out--`
47×	`difference-of-squares`
44×	`distribute-lft-out`
40×	`div-inv`
28×	`associate-/r/`
15×	`flip3--` `flip--`
13×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 430

Calls

4 calls:

37.0ms	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
1.0ms	(fma t z (* x y))
11.0ms	(/ a (- (+ (/ y z) b) y))
4.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

series627.0ms

Counts

4 → 12

Calls

4 calls:

388.0ms	(- (/ (fma t z (* x y)) (fma z (- b y) y)) (/ a (- (+ (/ y z) b) y)))
42.0ms	(fma t z (* x y))
49.0ms	(/ a (- (+ (/ y z) b) y))
148.0ms	(/ (fma t z (* x y)) (fma z (- b y) y))

simplify225.0ms

Algorithm

egg-herbie

Counts

442 → 442

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1051	16472
1	3018	12590
2	5001	11531

prune739.0ms

Filtered

442 candidates to 154 candidates (34.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	440	2	442
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	442	10	452

Merged error: 11.7b

Counts

452 → 10

regimes464.0ms

Accuracy

49.6% (3.2b remaining)

Error of 14.8b against oracle of 11.6b and baseline of 18.0b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	37
1	43	37
2	43	37

end0.0ms

sample767.0ms

Algorithm

intervals

Results

447.0ms

8427×

body

valid