Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	155×	body	160	valid
10.0ms	545×	pre	80	true
10.0ms	289×	body	80	nan
3.0ms	31×	body	320	valid
3.0ms	70×	body	80	valid

simplify12.0ms

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: 41.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite62.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
39.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735

prune250.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
28.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
153.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify160.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
0.2b	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
0.3b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-exp-log`
69×	`times-frac`
63×	`add-cbrt-cube`
50×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`div-exp`
31×	`prod-exp`
27×	`cbrt-undiv`
26×	`add-cube-cbrt`
17×	`cbrt-unprod`
13×	`associate-/r*`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/l*`
8×	`1-exp`
7×	`div-inv`
6×	`distribute-rgt-neg-in` `sqrt-prod` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `associate-*r/` `prod-diff` `associate-/r/`

Counts

4 → 160

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
26.0ms	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
48.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

series447.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
168.0ms	(/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))
107.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))

simplify44.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	946	2601
1	5001	2153

prune405.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.2b	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `fma-udef`

Counts

4 → 105

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
8.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
224.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
272.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
172.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	598	2144
1	3014	1804
2	5002	1754

prune389.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	31	13
2	31	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

348.0ms	4852×	body	160	valid
307.0ms	16218×	pre	80	true
282.0ms	8218×	body	80	nan
148.0ms	1351×	body	320	valid
65.0ms	1797×	body	80	valid