Details

sample368.0ms

Algorithm

intervals

Results

7.0ms	191×	body	80	valid
6.0ms	34×	body	2560	valid
5.0ms	36×	body	1280	valid
3.0ms	96×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

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: 38.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

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:

67.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

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

prune314.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.9b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.6b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
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 → 284

Calls

4 calls:

31.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
55.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
136.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
163.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify144.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505

prune603.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(/ a (* a c))
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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:

11.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(/ a (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ a (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (44.0ms)

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

prune295.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.9b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
27.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
630×	`add-sqr-sqrt`
629×	`*-un-lft-identity`
433×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
82×	`sqrt-prod`
70×	`distribute-rgt-neg-in`
60×	`prod-diff`
28×	`associate-/r*`
22×	`div-inv`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 569

Calls

4 calls:

29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
83.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
176.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
146.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

581 → 581

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1755	10833
1	5001	9431

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.5b

regimes235.0ms

Accuracy

79.2% (5.0b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 29.9b

bsearch86.0ms

Steps

Iters	Range		Point
6	4.231934083523606e+52	2.717919616353272e+53	1.50329899098719e+53
9	-1.1345718484749e-82	-1.1127264026331332e-88	-1.3696943711263392e-83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	38	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

195.0ms	1092×	body	2560	valid
188.0ms	5828×	body	80	valid
138.0ms	910×	body	1280	valid
82.0ms	2813×	body	80	nan
53.0ms	470×	body	640	valid
24.0ms	109×	body	5120	valid
20.0ms	235×	body	320	valid
7.0ms	126×	body	160	valid