Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	198×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	103×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	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: 34.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`associate-l`
2×	`flip3--` `fma-neg` `sqrt-div` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 25

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 3.0 a) c)
63.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify149.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	223	249
1	828	227
2	3445	217
3	5003	215

prune94.0ms

Filtered

37 candidates to 22 candidates (59.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	6	38

Merged error: 12.5b

Counts

38 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* b b) (- (* (* a c) 3.0)))
0.3b	(* (* a c) 3.0)
1.5b	(+ (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
23.0b	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-def` `flip3-+` `*-commutative` `flip-+`
2×	`+-commutative` `neg-sub0` `sqrt-div` `associate-l`
1×	`associate-+l-` `associate-+r-` `neg-mul-1` `pow1/2` `unsub-neg`

Counts

4 → 19

Calls

4 calls:

6.0ms	(+ (* b b) (- (* (* a c) 3.0)))
3.0ms	(* (* a c) 3.0)
6.0ms	(+ (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
6.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* b b) (- (* (* a c) 3.0)))
19.0ms	(* (* a c) 3.0)
77.0ms	(+ (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
69.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

simplify200.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	192	186
1	808	166
2	4700	151
3	5001	151

prune100.0ms

Filtered

31 candidates to 21 candidates (67.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	30	7	37

Merged error: 12.5b

Counts

37 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
4.5b	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))) (* 3.0 a))
10.2b	(/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0))))))
23.0b	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

10.0ms	(- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
19.0ms	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))) (* 3.0 a))
16.0ms	(/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0))))))
10.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
145.0ms	(/ (/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0)))))) (* 3.0 a))
185.0ms	(/ (* (* a c) 3.0) (- (- b) (sqrt (+ (* b b) (- (* (* a c) 3.0))))))
94.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	386	631
1	1538	560
2	5001	504

prune168.0ms

Filtered

51 candidates to 46 candidates (90.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	48	10	58

Merged error: 9.4b

Counts

58 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* b b) (- (* (* a c) 3.0)))
0.3b	(* (* a c) 3.0)
1.2b	(+ b (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
23.0b	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

3×	`flip3-+` `*-commutative` `flip-+`
2×	`+-commutative` `fma-def` `sqrt-div` `associate-l`
1×	`neg-sub0` `associate-+r-` `pow1/2` `unsub-neg`

Counts

4 → 17

Calls

4 calls:

6.0ms	(+ (* b b) (- (* (* a c) 3.0)))
4.0ms	(* (* a c) 3.0)
6.0ms	(+ b (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
7.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* b b) (- (* (* a c) 3.0)))
20.0ms	(* (* a c) 3.0)
82.0ms	(+ b (sqrt (+ (* b b) (- (* (* a c) 3.0)))))
72.0ms	(sqrt (+ (* b b) (- (* (* a c) 3.0))))

simplify159.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	169	175
1	659	157
2	3737	143
3	5001	141

prune68.0ms

Filtered

29 candidates to 21 candidates (72.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	32	7	39

Merged error: 7.3b

Counts

39 → 7

regimes262.0ms

Accuracy

95.4% (1.0b remaining)

Error of 8.3b against oracle of 7.3b and baseline of 29.4b

bsearch152.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	3.969902647964137e+110
8	-2.3862131106328103e-184	-9.444153407873295e-189	-1.8132672640965176e-188
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

3.969902647964137e+110

-2.3862131106328103e-184

-9.444153407873295e-189

-1.8132672640965176e-188

-2.083222696695489e+156

-8.927571262924557e+151

-1.3324370156406744e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	36
1	74	36
2	74	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

241.0ms	1092×	body	2560	valid
222.0ms	5870×	body	80	valid
159.0ms	873×	body	1280	valid
97.0ms	2852×	body	80	nan
65.0ms	452×	body	640	valid
31.0ms	117×	body	5120	valid
23.0ms	223×	body	320	valid
8.0ms	117×	body	160	valid