Details

sample280.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
6.0ms	29×	body	2560	valid
6.0ms	35×	body	1280	valid
2.0ms	71×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

45.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune233.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

49.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	448	823
1	1968	724
2	5003	682

prune233.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
2.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.4b	(* (/ 1 a) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(* (/ 1 a) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(* (/ 1 a) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	407	532
1	1938	427
2	5001	419

prune231.0ms

Filtered

94 candidates to 63 candidates (67.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(- (* b_2 b_2) (* a c))
2.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

32.0ms	(/ (+ (* (/ 1 a) 0) c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
2.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (* (/ 1 a) 0) c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	399	1173
1	1556	1049
2	5001	1033

prune239.0ms

Filtered

104 candidates to 74 candidates (71.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

regimes158.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.6b

bsearch112.0ms

Steps

Iters	Range		Point
6	4.659640959833754e+64	2.871891476161473e+65	2.4877801802577924e+65
8	1.241459029418506e-190	1.907704201430862e-187	1.2645910552421666e-190
7	-8.31287647374507e+123	-3.383610052221448e+122	-4.734236277817177e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample1.0s

Algorithm

intervals

Results

218.0ms	1111×	body	2560	valid
192.0ms	5797×	body	80	valid
138.0ms	879×	body	1280	valid
93.0ms	2947×	body	80	nan
55.0ms	458×	body	640	valid
29.0ms	113×	body	5120	valid
25.0ms	232×	body	320	valid
7.0ms	112×	body	160	valid