Details

sample288.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	189×	body	80	valid
4.0ms	27×	body	1280	valid
4.0ms	17×	body	640	valid
3.0ms	101×	body	80	nan
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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:

43.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

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))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

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

prune301.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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:

19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
164.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (99.0ms)

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

prune590.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.8b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

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:

19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
179.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
155.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

581 → 581

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1755	10832
1	5002	9428

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

853×	`times-frac`
555×	`add-sqr-sqrt`
554×	`*-un-lft-identity`
382×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
41×	`div-inv`
37×	`add-exp-log`
29×	`div-exp`
25×	`associate-/r*`
21×	`distribute-lft-neg-in`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`1-exp` `add-log-exp`
8×	`cbrt-undiv`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `associate-/l/`

Counts

4 → 518

Calls

4 calls:

36.0ms	(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ 1 1) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1830	9712
1	5001	8338

prune498.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes211.0ms

Accuracy

93.2% (1.6b remaining)

Error of 7.4b against oracle of 5.8b and baseline of 29.7b

bsearch132.0ms

Steps

Iters	Range		Point
7	7.8930669794294e+68	1.794276654474529e+70	1.7701741483501238e+70
9	-2.26016353878232e-246	-2.0825697103975006e-253	-4.062300732941478e-248
8	-6.30521239297407e+53	-2.0681333037085905e+50	-4.837192574744688e+53

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	42	23

end0.0ms

sample985.0ms

Algorithm

intervals

Results

196.0ms	1042×	body	2560	valid
186.0ms	5874×	body	80	valid
147.0ms	910×	body	1280	valid
92.0ms	2868×	body	80	nan
55.0ms	461×	body	640	valid
28.0ms	112×	body	5120	valid
23.0ms	230×	body	320	valid
8.0ms	104×	body	160	valid