Details

sample292.0ms

Algorithm

intervals

Results

14.0ms	195×	body	80	valid
11.0ms	33×	body	2560	valid
7.0ms	27×	body	1280	valid
4.0ms	65×	body	80	nan
4.0ms	5×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	6×	body	320	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

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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)
3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

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

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (+ 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)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
153.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
188.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.9b	(/ a (* a c))
23.6b	(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` `flip--` `associate-/l*`
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` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(/ a (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify129.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	277	415
1	944	374
2	4178	369
3	5002	368

prune174.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

12.4b	(cbrt (+ 0 (* a c)))
12.4b	(cbrt (+ 0 (* a c)))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip--` `flip-+`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* a c)))
2.0ms	(cbrt (+ 0 (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (+ 0 (* a c)))
70.0ms	(cbrt (+ 0 (* a c)))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	226	434
1	851	406
2	5001	386

prune277.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes180.0ms

Accuracy

88.1% (3.2b remaining)

Error of 9.1b against oracle of 5.9b and baseline of 32.4b

bsearch195.0ms

Steps

Iters	Range	Point
10	9.168682727753708e+124	1.4581761209996442e+140	1.2458828287346784e+132
10	-7.67245561718001e-112	-8.693838132238826e-123	-9.016549581630668e-123
8	-3.3081908876611885e+147	-2.274168596901093e+143	-2.760178712246234e+144

Iters

Range

Point

9.168682727753708e+124

1.4581761209996442e+140

1.2458828287346784e+132

-7.67245561718001e-112

-8.693838132238826e-123

-9.016549581630668e-123

-3.3081908876611885e+147

-2.274168596901093e+143

-2.760178712246234e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

433.0ms	5910×	body	80	valid
347.0ms	1059×	body	2560	valid
234.0ms	866×	body	1280	valid
184.0ms	2708×	body	80	nan
95.0ms	432×	body	640	valid
38.0ms	94×	body	5120	valid
35.0ms	210×	body	320	valid
14.0ms	116×	body	160	valid