Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

272×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune2.0ms

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: 26.0b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* a c) (* b d))
25.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`flip3-+` `flip-+`
2×	`fma-def` `associate-/r/` `associate-/l/`
1×	`+-commutative` `frac-2neg` `clear-num` `*-commutative` `div-inv`

Counts

2 → 12

Calls

2 calls:

4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify151.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	122	84
1	404	80
2	1407	79
3	4726	79
4	5001	79

prune61.0ms

Filtered

18 candidates to 15 candidates (83.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	7	19

Merged error: 25.4b

Counts

19 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.3b	(+ (* a c) (* b d))
25.5b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/`
5×	`flip3-+` `flip-+`
4×	`clear-num` `associate-/l/`
3×	`frac-2neg` `associate-/r*` `div-inv`
2×	`fma-def`
1×	`+-commutative` `*-commutative` `remove-double-div` `inv-pow`

Counts

3 → 25

Calls

3 calls:

8.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series222.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
33.0ms	(+ (* a c) (* b d))
54.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify68.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	164	153
1	598	142
2	2483	133
3	5001	132

prune104.0ms

Filtered

34 candidates to 27 candidates (79.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	33	8	41

Merged error: 25.3b

Counts

41 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
0.3b	(/ 1 (fma c c (* d d)))
0.6b	(/ 1 (+ (* a c) (* b d)))
25.5b	(/ (/ 1 (fma c c (* d d))) (/ 1 (+ (* a c) (* b d))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/` `div-inv`
5×	`frac-2neg` `clear-num`
4×	`flip3-+` `flip-+`
3×	`times-frac` `associate-/r*` `associate-/l/`
2×	`fma-def` `inv-pow`
1×	`+-commutative` `-commutative` `associate-/l`

Counts

4 → 31

Calls

4 calls:

4.0ms	(+ (* a c) (* b d))
2.0ms	(/ 1 (fma c c (* d d)))
4.0ms	(/ 1 (+ (* a c) (* b d)))
7.0ms	(/ (/ 1 (fma c c (* d d))) (/ 1 (+ (* a c) (* b d))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
45.0ms	(/ 1 (fma c c (* d d)))
27.0ms	(/ 1 (+ (* a c) (* b d)))
145.0ms	(/ (/ 1 (fma c c (* d d))) (/ 1 (+ (* a c) (* b d))))

simplify65.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	137	175
1	557	161
2	2162	160
3	5001	160

prune98.0ms

Filtered

43 candidates to 27 candidates (62.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Merged error: 25.3b

Counts

51 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* a c) (* b d))
0.2b	(- (* a c) (* b d))
25.7b	(/ (/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d))) (- (* a c) (* b d)))
30.6b	(/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative`
11×	`associate-/l/`
8×	`prod-diff`
5×	`flip3--` `flip--` `associate-/l*`
4×	`fma-neg` `associate-*r/`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`sub-neg` `associate-/r/`

Counts

4 → 40

Calls

4 calls:

4.0ms	(- (* a c) (* b d))
4.0ms	(- (* a c) (* b d))
9.0ms	(/ (/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d))) (- (* a c) (* b d)))
7.0ms	(/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* a c) (* b d))
38.0ms	(- (* a c) (* b d))
86.0ms	(/ (/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d))) (- (* a c) (* b d)))
145.0ms	(/ (* (fma a c (* b d)) (- (* a c) (* b d))) (fma c c (* d d)))

simplify129.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	171	313
1	720	306
2	4578	272
3	5001	271

prune121.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	50	10	60

Merged error: 18.2b

Counts

60 → 10

regimes230.0ms

Accuracy

31.5% (4.8b remaining)

Error of 23.9b against oracle of 19.1b and baseline of 26.1b

bsearch83.0ms

Steps

Iters	Range		Point
9	9.768553005369636e+133	6.764184952264426e+138	6.670795820110577e+138
9	-1.9658258378654302e+115	-1.957298096855346e+110	-1.9497673481821607e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	34	13
2	34	13

end0.0ms

sample492.0ms

Algorithm

intervals

Results

287.0ms

8441×

body

valid