Details

sample42.0ms

Algorithm

intervals

Results

8.0ms	201×	body	80	valid
7.0ms	23×	body	1280	valid
5.0ms	21×	body	2560	valid
3.0ms	87×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

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: 34.3b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

15.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune324.0ms

Filtered

169 candidates to 89 candidates (52.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Merged error: 8.3b

Counts

170 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

15.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193

prune305.0ms

Filtered

177 candidates to 89 candidates (50.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 8.2b

Counts

187 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
8.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	313	1367
1	1139	1090
2	5001	1064

prune322.0ms

Filtered

99 candidates to 78 candidates (78.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 8.2b

Counts

108 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
1.0b	(- (* b b) (* 4.0 (* a c)))
19.4b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
1.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt b)
44.0ms	(- (* b b) (* 4.0 (* a c)))
144.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	246	491
1	810	444
2	3581	426
3	5001	423

prune210.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 8.2b

Counts

77 → 9

regimes238.0ms

Accuracy

81.9% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 34.7b

bsearch114.0ms

Steps

Iters	Range		Point
7	6.184155830638016e+27	1.3306260697673677e+30	1.2919983862558445e+30
9	-7.983923007473122e-12	-3.7260100270962394e-17	-3.774134686283342e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	38	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

238.0ms	1038×	body	2560	valid
225.0ms	5870×	body	80	valid
176.0ms	900×	body	1280	valid
109.0ms	2910×	body	80	nan
66.0ms	434×	body	640	valid
34.0ms	115×	body	5120	valid
29.0ms	260×	body	320	valid
9.0ms	127×	body	160	valid