Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	201×	body	80	valid
6.0ms	31×	body	1280	valid
5.0ms	21×	body	2560	valid
4.0ms	103×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

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:

38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune297.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
116×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/l*`
16×	`distribute-rgt-neg-in`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-neg-in` `div-exp` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `sqrt-div` `div-sub` `sum-log` `flip--`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

42.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	646	2036
1	2495	1928
2	5001	1904

prune442.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

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:

38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune289.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`add-cube-cbrt`
31×	`times-frac`
25×	`add-cbrt-cube`
19×	`prod-diff`
16×	`sqrt-prod`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
8×	`add-log-exp`
7×	`fma-neg`
6×	`rec-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `flip--` `div-inv`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l/` `distribute-lft-out--`

Counts

4 → 142

Calls

4 calls:

20.0ms	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
25.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	705	1677
1	3374	1336
2	5002	1279

prune297.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

regimes264.0ms

Accuracy

87.2% (3.7b remaining)

Error of 9.2b against oracle of 5.5b and baseline of 34.1b

bsearch162.0ms

Steps

Iters	Range	Point
2	3.9431530817676045e+109	4.557375181159837e+109	4.019930844191633e+109
10	9.294290849485744e-131	6.48544897696183e-121	1.9238883452280037e-130
10	-1.5405955983178716e+163	-1.402598515452623e+153	-2.3044033969831823e+153

Iters

Range

Point

3.9431530817676045e+109

4.557375181159837e+109

4.019930844191633e+109

9.294290849485744e-131

6.48544897696183e-121

1.9238883452280037e-130

-1.5405955983178716e+163

-1.402598515452623e+153

-2.3044033969831823e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	28
1	48	28
2	48	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

266.0ms	1101×	body	2560	valid
239.0ms	5850×	body	80	valid
177.0ms	921×	body	1280	valid
108.0ms	2888×	body	80	nan
69.0ms	450×	body	640	valid
29.0ms	103×	body	5120	valid
26.0ms	228×	body	320	valid
10.0ms	121×	body	160	valid