Details

sample280.0ms

Algorithm

intervals

Results

6.0ms	31×	body	2560	valid
6.0ms	178×	body	80	valid
3.0ms	22×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	89×	body	80	nan
2.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune248.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
151.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune477.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.5b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.7b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
45.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
162.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
132.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1541	7329
1	5001	6762

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
13.5b	(/ (* a c) a)
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ (* a c) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify35.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	284	413
1	1182	378
2	5001	361

prune164.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

regimes192.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 32.6b

bsearch108.0ms

Steps

Iters	Range		Point
4	1.4117953071395708e+85	2.422703580179915e+85	1.9541965478093634e+85
10	-5.328377411097674e-143	-3.593908823127156e-156	-3.643707215764437e-156
5	-1.4095119951527517e+31	-5.823098213249637e+30	-8.87226991740961e+30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	39	22

end0.0ms

sample950.0ms

Algorithm

intervals

Results

200.0ms	1056×	body	2560	valid
195.0ms	5890×	body	80	valid
130.0ms	865×	body	1280	valid
83.0ms	2788×	body	80	nan
59.0ms	466×	body	640	valid
23.0ms	102×	body	5120	valid
20.0ms	227×	body	320	valid
6.0ms	106×	body	160	valid