Details

sample39.0ms

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	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: 33.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	265	247
1	959	236
2	3877	226
3	5002	225

prune119.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 5.9b

Counts

32 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite19.0ms

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

series213.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (82.0ms)

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

prune75.0ms

Filtered

26 candidates to 19 candidates (73.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	23	3	26
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	26	9	35

Merged error: 5.8b

Counts

35 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.9b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.0b	(- (* b b) (* 3.0 (* a c)))
24.1b	(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:

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

series215.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
46.0ms	(- (* b b) (* 3.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify84.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (81.0ms)

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

prune71.0ms

Filtered

26 candidates to 17 candidates (65.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	26	9	35

Merged error: 5.8b

Counts

35 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
0.9b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.0b	(- (* b b) (* (* 3.0 a) c))
24.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 23

Calls

4 calls:

10.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
6.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
5.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0))
76.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
46.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	218	230
1	833	220
2	4161	213
3	5002	213

prune83.0ms

Filtered

35 candidates to 28 candidates (80.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	35	9	44

Merged error: 5.8b

Counts

44 → 9

regimes201.0ms

Accuracy

87.9% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 34.3b

bsearch161.0ms

Steps

Iters	Range	Point
8	3.9532145147442873e+71	1.0218572913399418e+74	3.3124313189215764e+72
7	2.4861480825170347e-112	4.9053706167200877e-110	2.548256466828356e-112
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.4565416386855306e+144

Iters

Range

Point

3.9532145147442873e+71

1.0218572913399418e+74

3.3124313189215764e+72

2.4861480825170347e-112

4.9053706167200877e-110

2.548256466828356e-112

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.4565416386855306e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	28
1	46	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

261.0ms	1104×	body	2560	valid
239.0ms	5787×	body	80	valid
175.0ms	898×	body	1280	valid
110.0ms	2923×	body	80	nan
72.0ms	458×	body	640	valid
30.0ms	105×	body	5120	valid
26.0ms	226×	body	320	valid
9.0ms	123×	body	160	valid