Details

sample46.0ms

Algorithm

intervals

Results

8.0ms	31×	body	2560	valid
8.0ms	178×	body	80	valid
7.0ms	22×	body	1280	valid
4.0ms	23×	body	640	valid
4.0ms	89×	body	80	nan
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`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 → 157

Calls

4 calls:

44.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify81.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

56.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	656	3423
1	2594	2238
2	5001	2193

prune337.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 205

Calls

4 calls:

26.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify92.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	718	4221
1	3099	2976
2	5001	2863

prune338.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
6.4b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
141×	`prod-diff`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
51×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
33×	`distribute-lft-neg-in`
28×	`div-inv`
15×	`fma-neg`
11×	`neg-mul-1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 240

Calls

4 calls:

8.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
34.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
107.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
241.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify113.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	847	8136
1	2676	5939
2	5001	5143

prune401.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes235.0ms

Accuracy

79.2% (5.9b remaining)

Error of 11.7b against oracle of 5.8b and baseline of 34.1b

bsearch116.0ms

Steps

Iters	Range		Point
4	1.4117953071395708e+85	2.422703580179915e+85	2.3866645776898725e+85
5	-3.798273980088639e-127	-1.2883737028483634e-127	-3.704037072855455e-127
3	-1.701482398250145e-114	-1.332378922444805e-114	-1.3530354014836348e-114
5	-1.4095119951527517e+31	-5.823098213249637e+30	-5.921458590803185e+30

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

272.0ms	1057×	body	2560	valid
263.0ms	5889×	body	80	valid
185.0ms	862×	body	1280	valid
114.0ms	2791×	body	80	nan
77.0ms	466×	body	640	valid
34.0ms	102×	body	5120	valid
31.0ms	230×	body	320	valid
9.0ms	106×	body	160	valid