Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	180×	body	80	valid
8.0ms	35×	body	2560	valid
5.0ms	29×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	320	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `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 → 77

Calls

4 calls:

36.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune258.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

26.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* 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))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	533	1805
1	2544	1605
2	5002	1531

prune265.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
250×	`add-sqr-sqrt`
249×	`*-un-lft-identity`
149×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out--` `difference-of-squares`
37×	`div-inv`
28×	`sqrt-prod`
27×	`associate-/r*`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `flip--`
10×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 314

Calls

4 calls:

37.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* 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))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
42.0ms	(- (* 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))))

simplify77.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1231	6003
1	5001	5343

prune498.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `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 → 77

Calls

4 calls:

33.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* 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))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune214.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.1b

regimes269.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 34.0b

bsearch232.0ms

Steps

Iters	Range		Point
5	5.10808278574109e+145	1.867402505400959e+146	8.711101309869719e+145
10	-9.63247495909049e-100	-1.4236932931255447e-118	-4.052378358256912e-102
7	-2.3555604230285885e-90	-2.5832717791734895e-92	-8.212187268803771e-92
10	-6.255678465194574e+71	-1.2356841275142139e+58	-1.0366436397824178e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	34
1	56	34
2	56	34

end0.0ms

sample1.3s

Algorithm

intervals

Results

375.0ms	919×	body	1280	valid
262.0ms	1094×	body	2560	valid
227.0ms	5855×	body	80	valid
104.0ms	2917×	body	80	nan
61.0ms	415×	body	640	valid
29.0ms	102×	body	5120	valid
28.0ms	222×	body	320	valid
8.0ms	112×	body	160	valid