Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

263×

body

valid

simplify119.0ms

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

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: 19.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.5b	(+ (* x y) (* z (- t a)))
18.8b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite36.0ms

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))
7.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
11.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* z (- t a))
34.0ms	(* z (- b y))
43.0ms	(+ (* x y) (* z (- t a)))
301.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify76.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (61.0ms)

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

prune353.0ms

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: 19.0b

Counts

174 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(+ (* x y) (* z (- t a)))
0.8b	(/ 1 (+ y (* z (- b y))))
18.5b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite34.0ms

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:

7.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
4.0ms	(/ 1 (+ y (* z (- b y))))
11.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* z (- b y))
42.0ms	(+ (* x y) (* z (- t a)))
86.0ms	(/ 1 (+ y (* z (- b y))))
309.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (73.0ms)

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

prune374.0ms

Filtered

173 candidates to 106 candidates (61.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 19.0b

Counts

184 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x y (* t z))
0.8b	(/ 1 (+ y (* z (- b y))))
1.7b	(+ (fma x y (* t z)) (* z (- a)))
18.5b	(* (+ (fma x y (* t z)) (* z (- a))) (/ 1 (+ y (* z (- b y)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `distribute-rgt-neg-out` `cbrt-unprod` `fma-udef` `div-inv`
1×	`+-commutative` `associate-+l+` `pow-flip` `frac-2neg` `associate-r/` `unsub-neg` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 108

Calls

4 calls:

1.0ms	(fma x y (* t z))
4.0ms	(/ 1 (+ y (* z (- b y))))
3.0ms	(+ (fma x y (* t z)) (* z (- a)))
10.0ms	(* (+ (fma x y (* t z)) (* z (- a))) (/ 1 (+ y (* z (- b y)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma x y (* t z))
80.0ms	(/ 1 (+ y (* z (- b y))))
42.0ms	(+ (fma x y (* t z)) (* z (- a)))
286.0ms	(* (+ (fma x y (* t z)) (* z (- a))) (/ 1 (+ y (* z (- b y)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	374	1009
1	1969	833
2	5003	798

prune311.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	119	11	130

Merged error: 19.0b

Counts

130 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.4b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
0.5b	(+ (* x y) (* z (- t a)))
18.9b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

7.0ms	(* z (- b y))
11.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
6.0ms	(+ (* x y) (* z (- t a)))
7.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* z (- b y))
809.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
40.0ms	(+ (* x y) (* z (- t a)))
259.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify99.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	785	2479
1	3441	2063
2	5001	1964

prune390.0ms

Filtered

213 candidates to 121 candidates (56.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	213	11	224

Merged error: 19.0b

Counts

224 → 11

regimes385.0ms

Accuracy

0% (0.7b remaining)

Error of 23.7b against oracle of 23.0b and baseline of 23.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	31	10
2	32	10
3	32	10

end0.0ms

sample705.0ms

Algorithm

intervals

Results

419.0ms

8416×

body

valid

Details

sample26.0ms

simplify119.0ms

prune3.0ms

localize12.0ms

rewrite36.0ms

series416.0ms

simplify76.0ms

prune353.0ms

localize16.0ms

rewrite34.0ms

series472.0ms

simplify87.0ms

prune374.0ms

localize14.0ms

rewrite20.0ms

series446.0ms

simplify55.0ms

prune311.0ms

localize12.0ms

rewrite39.0ms

series1.1s

simplify99.0ms

prune390.0ms

regimes385.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample705.0ms

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