Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
8.0ms	195×	body	80	valid
6.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 32.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `clear-num` `*-commutative` `div-inv`

Counts

4 → 19

Calls

4 calls:

8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	269	246
1	985	235
2	3932	225
3	5002	224

prune103.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 5.8b

Counts

32 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b	(- (* b b) (* (* 4.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-/r*` `associate-/r/`
4×	`flip3--` `flip--`
3×	`associate-l` `associate-*l/`
2×	`sub-neg` `frac-2neg` `sqrt-div` `clear-num` `div-inv`
1×	`pow1/2` `*-commutative` `inv-pow`

Counts

4 → 23

Calls

4 calls:

12.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
6.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
79.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	220	230
1	837	220
2	3778	213
3	5001	213

prune97.0ms

Filtered

35 candidates to 28 candidates (80.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Merged error: 5.7b

Counts

42 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.1b	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-/l*`
8×	`associate-/r/` `*-commutative`
7×	`associate-/l/`
6×	`flip3--` `times-frac` `flip--`
5×	`div-inv`
4×	`associate-r`
3×	`frac-2neg` `clear-num`
2×	`sqrt-div` `associate-/r*`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow1/2`

Counts

4 → 38

Calls

4 calls:

5.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(/ (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms	(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	366	556
1	1449	509
2	5001	481

prune150.0ms

Filtered

50 candidates to 44 candidates (88.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	51	6	57

Merged error: 5.7b

Counts

57 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.3b	(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-*r/`
4×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `associate-l` `clear-num` `*-commutative` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `pow1/2` `associate-r` `un-div-inv` `div-inv`

Counts

4 → 22

Calls

4 calls:

5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	227	248
1	892	240
2	4596	225
3	5001	225

prune86.0ms

Filtered

34 candidates to 27 candidates (79.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	34	6	40

Merged error: 5.7b

Counts

40 → 6

regimes128.0ms

Accuracy

93.7% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 30.5b

bsearch191.0ms

Steps

Iters	Range	Point
8	2.996660094541056e+24	1.9235933371893114e+28	1.702453744110318e+28
8	-2.0939008728128375e-165	-4.8620484299604695e-170	-4.962069054079445e-170
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

2.996660094541056e+24

1.9235933371893114e+28

1.702453744110318e+28

-2.0939008728128375e-165

-4.8620484299604695e-170

-4.962069054079445e-170

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	28
1	49	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

263.0ms	1101×	body	2560	valid
237.0ms	5787×	body	80	valid
180.0ms	900×	body	1280	valid
114.0ms	2923×	body	80	nan
72.0ms	458×	body	640	valid
33.0ms	105×	body	5120	valid
28.0ms	227×	body	320	valid
9.0ms	123×	body	160	valid