Details

sample285.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
4.0ms	28×	body	1280	valid
4.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify13.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune299.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
3.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 210

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
140.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	761	3434
1	3490	3258
2	5002	3250

prune525.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
12.1b	(/ a (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 146

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ a (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	473	2541
1	1608	1646
2	5001	1557

prune285.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log`
69×	`div-exp`
65×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
61×	`prod-diff`
60×	`add-cube-cbrt`
34×	`sqrt-prod`
32×	`1-exp`
31×	`times-frac`
28×	`prod-exp`
25×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
17×	`rec-exp`
13×	`associate-/l*`
11×	`cbrt-undiv` `fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 209

Calls

4 calls:

17.0ms	(/ (/ 1 1) (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
10.0ms	(- (- 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)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (/ 1 1) (* (/ 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	900	3492
1	4010	2303
2	5001	2261

prune317.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

regimes145.0ms

Accuracy

94% (1.4b remaining)

Error of 6.7b against oracle of 5.2b and baseline of 28.9b

bsearch136.0ms

Steps

Iters	Range	Point
9	8.465625442272063e+58	8.825425083170634e+65	5.674292264829422e+63
7	-6.207156945681686e-303	-1.2633929192945347e-304	-1.6070331019441596e-304
10	-5.288637106878427e+83	-2.355035228211621e+66	-2.4276688444363324e+79

Iters

Range

Point

8.465625442272063e+58

8.825425083170634e+65

5.674292264829422e+63

-6.207156945681686e-303

-1.2633929192945347e-304

-1.6070331019441596e-304

-5.288637106878427e+83

-2.355035228211621e+66

-2.4276688444363324e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

203.0ms	1083×	body	2560	valid
194.0ms	5784×	body	80	valid
145.0ms	926×	body	1280	valid
94.0ms	2977×	body	80	nan
54.0ms	453×	body	640	valid
29.0ms	106×	body	5120	valid
25.0ms	258×	body	320	valid
7.0ms	119×	body	160	valid