Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

267×

body

valid

simplify134.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

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: 21.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- b y))
1.6b	(+ (* x y) (* z (- t a)))
20.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

6.0ms	(+ y (* z (- b y)))
7.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
9.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ y (* z (- b y)))
37.0ms	(* z (- b y))
44.0ms	(+ (* x y) (* z (- t a)))
338.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify81.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	602	1288
1	2282	956
2	5001	937

prune460.0ms

Filtered

165 candidates to 109 candidates (66.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	12	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Merged error: 20.7b

Counts

166 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
1.0b	(fma x y (* z (- t a)))
20.6b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`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`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma z (- b y) y)
8.0ms	(* z (- t a))
1.0ms	(fma x y (* z (- t a)))
3.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series450.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma z (- b y) y)
37.0ms	(* z (- t a))
50.0ms	(fma x y (* z (- t a)))
338.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify51.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	774
1	1107	590
2	5001	584

prune284.0ms

Filtered

107 candidates to 67 candidates (62.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Merged error: 20.7b

Counts

119 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.7b	(/ 1 (+ y (* z (- b y))))
1.6b	(+ (* x y) (* z (- t a)))
20.4b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

8.0ms	(* z (- b y))
5.0ms	(/ 1 (+ y (* z (- b y))))
6.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* z (- b y))
84.0ms	(/ 1 (+ y (* z (- b y))))
47.0ms	(+ (* x y) (* z (- t a)))
341.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011

prune390.0ms

Filtered

173 candidates to 104 candidates (60.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	173	12	185

Merged error: 20.7b

Counts

185 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b y))
0.6b	(cbrt (- b y))
1.6b	(+ (* x y) (* z (- t a)))
20.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt`
22×	`associate-+r+`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`sub-neg` `flip3--` `pow1/3` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (- b y))
3.0ms	(cbrt (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (- b y))
159.0ms	(cbrt (- b y))
48.0ms	(+ (* x y) (* z (- t a)))
342.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* z (* (cbrt (- b y)) (cbrt (- b y)))) (cbrt (- b y)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	517	1258
1	1564	1102
2	5002	1055

prune379.0ms

Filtered

115 candidates to 93 candidates (80.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	114	13	127

Merged error: 20.7b

Counts

127 → 13

regimes507.0ms

Accuracy

0% (0.6b remaining)

Error of 23.2b against oracle of 22.6b and baseline of 23.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	6
1	20	6
2	20	6

end0.0ms

sample720.0ms

Algorithm

intervals

Results

423.0ms

8390×

body

valid