Details

sample40.0ms

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

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

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: 32.9b

Counts

2 → 1

localize11.0ms

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))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-r`
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:

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

series296.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify139.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	318	329
1	1134	301
2	4750	289
3	5001	289

prune120.0ms

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

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))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
5×	`associate-/r*` `associate-/r/`
4×	`flip3--` `associate-r` `flip--`
3×	`associate-l` `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:

14.0ms	(/ 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))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
81.0ms	(- (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))))

simplify129.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	266	306
1	977	286
2	4469	273
3	5001	273

prune112.0ms

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

localize18.0ms

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:

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

series476.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
179.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	372	555
1	1701	490
2	5001	455

prune159.0ms

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

localize15.0ms

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))))

rewrite37.0ms

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))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
126.0ms	(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
105.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	617	894
1	2620	768
2	5001	763

prune238.0ms

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

regimes130.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.3b

bsearch184.0ms

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

sample1.2s

Algorithm

intervals

Results

266.0ms	1101×	body	2560	valid
238.0ms	5787×	body	80	valid
174.0ms	900×	body	1280	valid
119.0ms	2923×	body	80	nan
70.0ms	458×	body	640	valid
35.0ms	105×	body	5120	valid
26.0ms	227×	body	320	valid
9.0ms	123×	body	160	valid