Details

sample278.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
6.0ms	32×	body	2560	valid
4.0ms	103×	body	80	nan
3.0ms	23×	body	1280	valid
2.0ms	19×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify16.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.7b

Counts

2 → 1

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))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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:

23.0ms	(/ (+ (- 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)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(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

prune272.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 6.1b

Counts

113 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

17.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(+ (- 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)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	479	897
1	2066	778
2	5003	729

prune252.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	117	10	127

Merged error: 6.1b

Counts

127 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 196

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	658	2518
1	2948	2155
2	5002	2004

prune280.0ms

Filtered

208 candidates to 104 candidates (50.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	207	11	218

Merged error: 6.1b

Counts

218 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
507×	`add-sqr-sqrt`
420×	`*-un-lft-identity`
334×	`add-cube-cbrt`
86×	`difference-of-squares`
58×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
19×	`prod-diff`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
7×	`fma-neg`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 457

Calls

4 calls:

24.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

469 → 469

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1775	7995
1	5002	7502

prune800.0ms

Filtered

469 candidates to 265 candidates (56.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	469	0	469
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	469	11	480

Merged error: 6.1b

Counts

480 → 11

regimes237.0ms

Accuracy

82% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 33.9b

bsearch90.0ms

Steps

Iters	Range		Point
10	2.319058093766752e-122	4.8666627780759835e-109	5.807942761752216e-116
8	-2.7230751788376357e+101	-3.525651047217798e+97	-8.43375075978364e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample989.0ms

Algorithm

intervals

Results

206.0ms	1056×	body	2560	valid
187.0ms	5771×	body	80	valid
150.0ms	956×	body	1280	valid
87.0ms	2944×	body	80	nan
56.0ms	480×	body	640	valid
27.0ms	115×	body	5120	valid
20.0ms	227×	body	320	valid
7.0ms	111×	body	160	valid