Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
6.0ms	179×	body	80	valid
5.0ms	29×	body	1280	valid
3.0ms	85×	body	80	nan
2.0ms	3×	body	160	valid
2.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

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: 36.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
50.0ms	(- (* b b) (* (* 3.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune290.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 5.0b

Counts

103 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.1b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
15.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
189.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
182.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify171.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune516.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	240	4	244
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	241	12	253

Merged error: 4.8b

Counts

253 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0b	(/ (* 3.0 a) (* 3.0 (* a c)))
23.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	598	3041
1	3053	1925
2	5002	1816

prune285.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	163	11	174

Merged error: 4.8b

Counts

174 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.0b	(- (* b b) (* (* 3.0 a) c))
2.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 162

Calls

4 calls:

17.0ms	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
50.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	614	3343
1	2377	2171
2	5001	2121

prune254.0ms

Filtered

174 candidates to 87 candidates (50.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	174	11	185

Merged error: 4.8b

Counts

185 → 11

regimes289.0ms

Accuracy

92.2% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 29.8b

bsearch166.0ms

Steps

Iters	Range		Point
9	14028.172733867412	3007116902181.375	2947728123750.7354
8	-4.654091770266614e-259	-1.1349992526466847e-263	-1.3969863832568379e-263
8	-3.346688072492859e+118	-7.406473594041322e+115	-1.0306858894842368e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

224.0ms	1099×	body	2560	valid
211.0ms	5799×	body	80	valid
152.0ms	888×	body	1280	valid
95.0ms	2953×	body	80	nan
66.0ms	468×	body	640	valid
29.0ms	118×	body	5120	valid
21.0ms	214×	body	320	valid
7.0ms	111×	body	160	valid

Details

sample39.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite28.0ms

series314.0ms

simplify51.0ms

prune290.0ms

localize14.0ms

rewrite55.0ms

series552.0ms

simplify171.0ms

prune516.0ms

localize14.0ms

rewrite31.0ms

series223.0ms

simplify105.0ms

prune285.0ms

localize12.0ms

rewrite41.0ms

series381.0ms

simplify77.0ms

prune254.0ms

regimes289.0ms

bsearch166.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling