Details

sample324.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
6.0ms	186×	body	80	valid
4.0ms	28×	body	1280	valid
2.0ms	86×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

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:

64.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
30.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(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

prune237.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.1b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
125.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
152.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune502.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
36×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`cbrt-prod`
20×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`cbrt-undiv` `div-exp`
13×	`sqrt-prod`
8×	`cbrt-div` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
7×	`pow1` `flip3--` `flip--`
6×	`sqrt-div`
5×	`div-inv`
4×	`distribute-rgt-neg-in` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r*`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 135

Calls

4 calls:

111.0ms	(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	697	3506
1	3198	3279
2	5002	3261

prune469.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0b	(/ a (* a c))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ a (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ a (* a c))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify136.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	294	462
1	1070	416
2	4891	406
3	5002	406

prune175.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes278.0ms

Accuracy

83.8% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 32.0b

bsearch82.0ms

Steps

Iters	Range		Point
10	7.028227535098625e-82	3.98361551741597e-66	9.800093806317492e-70
8	-5.3591540899030606e+132	-7.727081080122102e+128	-4.2967115055034046e+132

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample995.0ms

Algorithm

intervals

Results

181.0ms	5865×	body	80	valid
179.0ms	1051×	body	2560	valid
129.0ms	933×	body	1280	valid
77.0ms	2810×	body	80	nan
52.0ms	457×	body	640	valid
28.0ms	113×	body	5120	valid
19.0ms	232×	body	320	valid
7.0ms	120×	body	160	valid