Details

sample272.0ms

Algorithm

intervals

Results

6.0ms	31×	body	2560	valid
6.0ms	178×	body	80	valid
3.0ms	22×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	89×	body	80	nan
2.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

52.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 169

Calls

4 calls:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5001	1940

prune331.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

27.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
74.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune375.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))
20.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	159	467
1	511	446
2	1701	440
3	5002	431

prune277.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.9b

regimes218.0ms

Accuracy

79% (6.0b remaining)

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

bsearch94.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample991.0ms

Algorithm

intervals

Results

204.0ms	1056×	body	2560	valid
199.0ms	5890×	body	80	valid
138.0ms	865×	body	1280	valid
86.0ms	2788×	body	80	nan
56.0ms	466×	body	640	valid
24.0ms	102×	body	5120	valid
21.0ms	227×	body	320	valid
6.0ms	106×	body	160	valid