Details

sample278.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
7.0ms	35×	body	2560	valid
5.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`prod-diff`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `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 → 24

Calls

4 calls:

6.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	258	227
1	862	209
2	3117	196
3	5001	182

prune109.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	7	37

Merged error: 5.8b

Counts

37 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 33

Calls

4 calls:

9.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
4.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	279	358
1	1113	309
2	5001	280

prune115.0ms

Filtered

45 candidates to 32 candidates (71.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	46	6	52

Merged error: 5.8b

Counts

52 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.9b	(/ (+ 0 (* 2 (* a c))) (* a 2))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 26

Calls

4 calls:

5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (+ 0 (* 2 (* a c))) (* a 2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (+ 0 (* 2 (* a c))) (* a 2))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	247	214
1	1056	191
2	5001	176

prune96.0ms

Filtered

38 candidates to 27 candidates (71.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	38	6	44

Merged error: 5.7b

Counts

44 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

Calls

4 calls:

5.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
31.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	217	234
1	721	221
2	2422	202
3	5001	192

prune79.0ms

Filtered

36 candidates to 27 candidates (75.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	36	6	42

Merged error: 5.7b

Counts

42 → 6

regimes168.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.3b

bsearch149.0ms

Steps

Iters	Range	Point
8	1.31764557419022e+108	4.7801703725873666e+111	5.8672354253329364e+110
10	-3.3872652091741538e-211	-3.093295365731255e-225	-8.781062788627254e-225
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

1.31764557419022e+108

4.7801703725873666e+111

5.8672354253329364e+110

-3.3872652091741538e-211

-3.093295365731255e-225

-8.781062788627254e-225

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample999.0ms

Algorithm

intervals

Results

216.0ms	1105×	body	2560	valid
189.0ms	5783×	body	80	valid
137.0ms	898×	body	1280	valid
91.0ms	2921×	body	80	nan
58.0ms	460×	body	640	valid
25.0ms	105×	body	5120	valid
23.0ms	226×	body	320	valid
8.0ms	124×	body	160	valid