Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	278×	body	80	valid
4.0ms	97×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

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: 20.2b

Counts

2 → 1

localize117.0ms

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))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`prod-diff`
4×	`flip3--` `sqrt-div` `associate-l` `flip--`
3×	`fma-neg`
2×	`sub-neg` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-mul-1`

Counts

4 → 26

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	222	311
1	822	288
2	3420	276
3	5001	242

prune139.0ms

Filtered

38 candidates to 25 candidates (65.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	32	6	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	6	39

Merged error: 8.4b

Counts

39 → 6

localize117.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.3b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.0b	(/ (* a c) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
4×	`div-sub` `associate-l`
3×	`flip3--` `flip--`
2×	`sub-neg` `frac-2neg` `fma-neg` `sqrt-div` `clear-num` `associate-/r` `div-inv` `associate-/l/` `associate-/l` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow1/2`

Counts

4 → 33

Calls

4 calls:

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

series194.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
60.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
19.0ms	(/ (* a c) b)
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	278	294
1	1025	282
2	4358	273
3	5001	273

prune141.0ms

Filtered

45 candidates to 27 candidates (60.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	44	7	51

Merged error: 6.8b

Counts

51 → 7

localize114.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
2×	`flip3--` `flip3-+` `fma-neg` `sqrt-div` `associate-/r/` `flip--` `flip-+` `associate-/l*`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 29

Calls

4 calls:

8.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	277	323
1	933	290
2	3601	278
3	5001	276

prune138.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	41	7	48

Merged error: 6.6b

Counts

48 → 7

localize116.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`associate-l`
3×	`associate-r/` `associate-r*`
2×	`flip3--` `flip3-+` `fma-neg` `sqrt-div` `clear-num` `associate-/r/` `un-div-inv` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `div-inv`

Counts

4 → 33

Calls

4 calls:

9.0ms	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify34.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	289	303
1	1063	270
2	5001	261

prune121.0ms

Filtered

45 candidates to 29 candidates (64.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	45	7	52

Merged error: 6.6b

Counts

52 → 7

regimes203.0ms

Accuracy

92.6% (1.1b remaining)

Error of 7.4b against oracle of 6.3b and baseline of 20.6b

bsearch240.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	2.6429722002179594e+103
8	1.2144307814005946e-307	1.5667111089934007e-304	1.2324305000920097e-307
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

2.6429722002179594e+103

1.2144307814005946e-307

1.5667111089934007e-304

1.2324305000920097e-307

-1.2994787762702041e+157

-3.0529494422842112e+156

-3.0812943354752785e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	68
1	63	68

end0.0ms

sample845.0ms

Algorithm

intervals

Results

456.0ms	8757×	body	80	valid
141.0ms	2939×	body	80	nan