Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	33×	body	2560	valid
6.0ms	197×	body	80	valid
4.0ms	27×	body	1280	valid
3.0ms	116×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

34.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune239.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

33.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune237.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
7.0b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

7.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
34.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	392	1007
1	1190	962
2	4404	947
3	5002	947

prune261.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
10.0b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`add-exp-log` `times-frac` `associate-r`
10×	`sqrt-div`
9×	`sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`associate-l` `frac-sub` `unswap-sqr`
4×	`frac-times` `associate-*l/` `prod-exp`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `distribute-rgt-out--` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 95

Calls

4 calls:

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

series275.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
83.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	514	978
1	1930	901
2	5001	876

prune248.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.6b

regimes234.0ms

Accuracy

88.5% (3.4b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 35.0b

bsearch135.0ms

Steps

Iters	Range	Point
9	2.6683347110001497e+63	3.895668027475672e+69	2.5329642823852832e+69
6	-5.609109599303715e-148	-3.717393021040523e-149	-6.734488033758564e-149
10	-1.0670255160813602e+56	-9.302435528785865e+43	-1.6951520440902905e+47

Iters

Range

Point

2.6683347110001497e+63

3.895668027475672e+69

2.5329642823852832e+69

-5.609109599303715e-148

-3.717393021040523e-149

-6.734488033758564e-149

-1.0670255160813602e+56

-9.302435528785865e+43

-1.6951520440902905e+47

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	28
1	60	28
2	60	28

end0.0ms

sample979.0ms

Algorithm

intervals

Results

202.0ms	1048×	body	2560	valid
185.0ms	5813×	body	80	valid
143.0ms	930×	body	1280	valid
90.0ms	2899×	body	80	nan
55.0ms	471×	body	640	valid
27.0ms	110×	body	5120	valid
20.0ms	226×	body	320	valid
7.0ms	115×	body	160	valid