Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	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

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

7.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
5.0ms	(+ (- 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)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
92.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify133.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	322	329
1	1151	301
2	4762	289
3	5001	289

prune136.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	35	7	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	7	43

Merged error: 5.8b

Counts

43 → 7

localize14.0ms

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)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 33

Calls

4 calls:

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

series340.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
43.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	271	306
1	990	286
2	4474	273
3	5001	273

prune103.0ms

Filtered

45 candidates to 29 candidates (64.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	45	7	52

Merged error: 5.7b

Counts

52 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 35

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	383	555
1	1845	490
2	5002	456

prune144.0ms

Filtered

47 candidates to 41 candidates (87.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	47	7	54

Merged error: 5.7b

Counts

54 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
10.4b	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
24.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-/l/`
33×	`associate-/r/`
28×	`times-frac`
19×	`*-commutative`
16×	`associate-/l*`
14×	`div-inv`
13×	`associate-/r*`
10×	`frac-2neg` `clear-num`
6×	`flip3--` `flip--`
4×	`div-sub`
2×	`associate--l-` `neg-sub0` `sqrt-div`
1×	`neg-mul-1` `sub-neg` `pow1/2` `fma-neg`

Counts

4 → 71

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
9.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
119.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))) (* 2.0 a))
227.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 4.0) (* a c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	618	894
1	2656	768
2	5002	763

prune220.0ms

Filtered

83 candidates to 66 candidates (79.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	84	6	90

Merged error: 5.7b

Counts

90 → 6

regimes129.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.3b

bsearch189.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	2.739269029802694e+102
8	-2.0939008728128375e-165	-4.8620484299604695e-170	-4.962069054079445e-170
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

2.739269029802694e+102

-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	47	27
1	49	27
2	49	27

end0.0ms

sample1.1s

Algorithm

intervals

Results

252.0ms	1101×	body	2560	valid
223.0ms	5787×	body	80	valid
167.0ms	900×	body	1280	valid
108.0ms	2923×	body	80	nan
66.0ms	458×	body	640	valid
32.0ms	227×	body	320	valid
31.0ms	105×	body	5120	valid
9.0ms	123×	body	160	valid