Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
7.0ms	36×	body	1280	valid
7.0ms	165×	body	80	valid
3.0ms	87×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize17.0ms

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))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

36.0ms	(/ (+ (- 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))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
60.0ms	(- (* b b) (* (* 4.0 a) c))
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune362.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

53.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
58.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	514	1012
1	2322	856
2	5001	843

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

40.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
58.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	485	1246
1	1921	1004
2	5002	972

prune316.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

25.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
87.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	269	1448
1	1027	1098
2	5002	1038

prune381.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes277.0ms

Accuracy

81.7% (5.1b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 33.7b

bsearch114.0ms

Steps

Iters	Range		Point
9	2.365685850767504e-168	1.2053288471691685e-161	1.1860189201379418e-161
6	-2.0136180636941443e+142	-1.4127342237564056e+141	-2.61268387266151e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	31	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

243.0ms	5914×	body	80	valid
235.0ms	1025×	body	2560	valid
174.0ms	891×	body	1280	valid
113.0ms	2997×	body	80	nan
66.0ms	450×	body	640	valid
33.0ms	107×	body	5120	valid
23.0ms	209×	body	320	valid
12.0ms	104×	body	160	valid