Details

sample291.0ms

Algorithm

intervals

Results

11.0ms	209×	body	80	valid
7.0ms	32×	body	1280	valid
6.0ms	25×	body	2560	valid
4.0ms	103×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify15.0ms

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

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: 28.1b

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)
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

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

prune266.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 3.5b

Counts

113 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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)))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (65.0ms)

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

prune293.0ms

Filtered

208 candidates to 104 candidates (50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	204	4	208
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	207	9	216

Merged error: 3.5b

Counts

216 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

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:

21.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

469 → 469

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1775	7995
1	5002	7078

prune573.0ms

Filtered

469 candidates to 189 candidates (40.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	468	1	469
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	469	9	478

Merged error: 3.5b

Counts

478 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))
17.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 88

Calls

4 calls:

8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	227	580
1	813	526
2	2889	504
3	5002	498

prune278.0ms

Filtered

100 candidates to 86 candidates (86.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	100	9	109

Merged error: 3.5b

Counts

109 → 9

regimes173.0ms

Accuracy

88.7% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 33.8b

bsearch142.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	2.5096626454411205e+56
10	8.752895080382474e-191	7.198562597133285e-172	2.5184045435465955e-179
4	-2.2709498629311444e+153	-1.3123487377944479e+153	-1.5396067403637575e+153

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

2.5096626454411205e+56

8.752895080382474e-191

7.198562597133285e-172

2.5184045435465955e-179

-2.2709498629311444e+153

-1.3123487377944479e+153

-1.5396067403637575e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	43	24
2	43	24

end0.0ms

sample1.3s

Algorithm

intervals

Results

262.0ms	1054×	body	2560	valid
260.0ms	5869×	body	80	valid
184.0ms	896×	body	1280	valid
122.0ms	2921×	body	80	nan
77.0ms	460×	body	640	valid
32.0ms	106×	body	5120	valid
26.0ms	219×	body	320	valid
11.0ms	106×	body	160	valid