Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	37×	body	2560	valid
8.0ms	197×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune296.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
51.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	556	1665
1	2664	1442
2	5002	1371

prune330.0ms

Filtered

146 candidates to 91 candidates (62.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
4.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
50.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	402	977
1	1485	896
2	5001	874

prune341.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.9b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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) (* 4.0 (* a c)))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
161.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
193.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860

prune548.0ms

Filtered

244 candidates to 140 candidates (57.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.9b

regimes200.0ms

Accuracy

85.9% (4.0b remaining)

Error of 9.7b against oracle of 5.7b and baseline of 33.8b

bsearch196.0ms

Steps

Iters	Range		Point
6	6254161.133583045	42925490.781275615	40732783.80363628
9	3.6472374174305276e-171	1.5912567937714158e-163	1.5568198144016078e-163
10	-4.4721271386820616e+151	-9.712280864301115e+136	-7.700313305414632e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	34
1	52	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

247.0ms	5938×	body	80	valid
246.0ms	1045×	body	2560	valid
160.0ms	852×	body	1280	valid
110.0ms	2870×	body	80	nan
65.0ms	442×	body	640	valid
32.0ms	112×	body	5120	valid
28.0ms	226×	body	320	valid
9.0ms	119×	body	160	valid