Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
7.0ms	193×	body	80	valid
4.0ms	99×	body	80	nan
3.0ms	16×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.3b

localize18.0ms

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)))
1.3b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite101.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (+ (- 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)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune220.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

16.0ms	(- (* b b) (* 4.0 (* a c)))
118.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
100.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	628	2579
1	2954	2333
2	5001	2320

prune389.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
10.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`flip3--` `sqrt-div` `associate-/r*` `flip--`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 80

Calls

4 calls:

34.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
11.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
83.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	393	1605
1	1745	1359
2	5002	1282

prune330.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
15.3b	(/ (* 2.0 a) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

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:

24.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (46.0ms)

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

prune176.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes188.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.8b

bsearch139.0ms

Steps

Iters	Range	Point
7	2.5938763934072053e+128	6.455437820905187e+129	4.0598649397170545e+128
6	-2.891186526843327e-238	-3.8162486351435958e-239	-5.269237409668851e-239
7	-3.11898899158337e+65	-2.3526715177838076e+63	-3.0609761389176743e+65

Iters

Range

Point

2.5938763934072053e+128

6.455437820905187e+129

4.0598649397170545e+128

-2.891186526843327e-238

-3.8162486351435958e-239

-5.269237409668851e-239

-3.11898899158337e+65

-2.3526715177838076e+63

-3.0609761389176743e+65

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	37
1	49	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

234.0ms	5908×	body	80	valid
228.0ms	1025×	body	2560	valid
149.0ms	843×	body	1280	valid
106.0ms	2941×	body	80	nan
65.0ms	457×	body	640	valid
37.0ms	119×	body	5120	valid
24.0ms	228×	body	320	valid
9.0ms	101×	body	160	valid