Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
9.0ms	198×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	103×	body	80	nan
3.0ms	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	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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

localize13.0ms

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)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3--` `sqrt-div` `associate-l` `*-commutative` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 14

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
5.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	174	166
1	670	161
2	2638	153
3	5001	152

prune74.0ms

Filtered

26 candidates to 19 candidates (73.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	6	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	7	27

Merged error: 12.5b

Counts

27 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 14

Calls

4 calls:

5.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
5.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* 3.0 (* a c)))
23.0ms	(* 3.0 (* a c))
73.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify79.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	171	166
1	637	161
2	2496	153
3	5002	152

prune64.0ms

Filtered

26 candidates to 16 candidates (61.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	27	6	33

Merged error: 12.5b

Counts

33 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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) (* 3.0 (* a c)))))
10.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
8.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
142.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
305.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
70.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	361	556
1	1366	509
2	5001	476

prune157.0ms

Filtered

50 candidates to 45 candidates (90.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	45	11	56

Merged error: 9.4b

Counts

56 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3.0 c) (* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a)))
1.2b	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
6.8b	(* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a))
23.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

10.0ms	(/ (* 3.0 c) (* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a)))
5.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
11.0ms	(* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (* 3.0 c) (* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
85.0ms	(* (* 3.0 a) (/ (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))) a))
66.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	360	467
1	1528	424
2	5001	419

prune149.0ms

Filtered

56 candidates to 50 candidates (89.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	55	12	67

Merged error: 6.8b

Counts

67 → 12

regimes204.0ms

Accuracy

79.1% (5.1b remaining)

Error of 11.5b against oracle of 6.5b and baseline of 30.7b

bsearch116.0ms

Steps

Iters	Range		Point
9	3.1545612030570996e+46	9.408773056633495e+53	8.47915506480201e+53
8	-1.4458363231597228e-72	-3.604255717438821e-77	-3.579252055600559e-75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	21
1	47	21
2	47	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

237.0ms	1092×	body	2560	valid
217.0ms	5870×	body	80	valid
154.0ms	873×	body	1280	valid
98.0ms	2852×	body	80	nan
63.0ms	452×	body	640	valid
31.0ms	117×	body	5120	valid
23.0ms	223×	body	320	valid
8.0ms	117×	body	160	valid