Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	189×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	87×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize14.0ms

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)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

34.0ms	(/ (+ (- 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))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune239.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
30.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	640	2692
1	2944	2439
2	5001	2426

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	413	627
1	2231	543
2	5001	535

prune229.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (/ 0.5 c) (- (- 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)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod` `cbrt-unprod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

22.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (/ 1 1) (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	660	1395
1	3283	1186
2	5001	1152

prune248.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

regimes139.0ms

Accuracy

84.5% (3.8b remaining)

Error of 9.1b against oracle of 5.3b and baseline of 29.7b

bsearch177.0ms

Steps

Iters	Range		Point
5	5.10808278574109e+145	1.867402505400959e+146	9.864067237590881e+145
10	-9.63247495909049e-100	-1.4236932931255447e-118	-1.6465862921393153e-101
7	-2.3555604230285885e-90	-2.5832717791734895e-92	-2.9346814112434403e-92
3	-2.6939693106550122e-64	-1.9710978016715664e-64	-2.648789841343547e-64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	39
1	57	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

245.0ms	1073×	body	2560	valid
217.0ms	5759×	body	80	valid
164.0ms	914×	body	1280	valid
107.0ms	2900×	body	80	nan
69.0ms	451×	body	640	valid
28.0ms	100×	body	5120	valid
24.0ms	229×	body	320	valid
9.0ms	132×	body	160	valid