Details

sample59.0ms

Algorithm

intervals

Results

14.0ms	153×	body	160	valid
9.0ms	270×	body	80	nan
9.0ms	526×	pre	80	true
4.0ms	41×	body	320	valid
2.0ms	62×	body	80	valid

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

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))
37.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite114.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

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

prune253.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

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))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite200.0ms

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:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
88.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
157.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
197.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (116.0ms)

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

prune556.0ms

Pruning

8 alts after pruning (8 fresh and 0 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))
0.3b	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite68.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 4.0 a) c))
243.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
175.0ms	(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
288.0ms	(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify110.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	598	2143
1	3014	1804
2	5002	1754

prune427.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

312×	`add-exp-log`
142×	`div-exp`
138×	`add-cbrt-cube`
137×	`prod-exp`
121×	`prod-diff`
102×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
57×	`cbrt-unprod`
48×	`cbrt-undiv`
40×	`1-exp`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
33×	`times-frac`
16×	`rec-exp`
14×	`associate-/l*`
12×	`neg-mul-1`
7×	`associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3--` `associate-l` `associate-/r/` `flip--` `div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`fma-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 327

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
155.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
94.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1655	9053
1	5001	6430

prune405.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

330.0ms	4819×	body	160	valid
280.0ms	8303×	body	80	nan
273.0ms	16303×	pre	80	true
142.0ms	1349×	body	320	valid
65.0ms	1832×	body	80	valid