Details

sample52.0ms

Algorithm

intervals

Results

30.0ms	282×	body	80	valid
6.0ms	79×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize114.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
2.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	406	2988
1	1431	1956
2	5002	1869

prune379.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

localize118.0ms

Local error

Found 4 expressions with local error:

9.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 76

Calls

4 calls:

9.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	249	756
1	969	641
2	4038	626
3	5001	624

prune404.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.2b

localize118.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
3.4b	(/ (* a c) b)
3.5b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff`

Counts

4 → 82

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(/ (* a c) b)
18.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(/ (* a c) b)
79.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	454	650
1	2083	569
2	5001	564

prune343.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize113.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(- (* b b) (* (* 4.0 a) c))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
189.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	400	830
1	1671	721
2	5002	704

prune338.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes162.0ms

Accuracy

92.9% (1.0b remaining)

Error of 7.5b against oracle of 6.5b and baseline of 21.1b

bsearch165.0ms

Steps

Iters	Range		Point
9	1.0966316111626227e+109	8.247031634266059e+117	1.2199100360588728e+112
7	-1.6124847451767553e+146	-7.05891254188438e+144	-7.021208029070988e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	51
1	59	51

end0.0ms

sample1.3s

Algorithm

intervals

Results

813.0ms	8735×	body	80	valid
248.0ms	2992×	body	80	nan