Details

sample112.0ms

Algorithm

intervals

Results

30.0ms	112×	body	320	valid
21.0ms	242×	body	80	nan
18.0ms	498×	pre	80	true
15.0ms	91×	body	160	valid
6.0ms	20×	body	640	valid
3.0ms	33×	body	80	valid

simplify13.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite53.0ms

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))
33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune242.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 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)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
147.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify124.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	674	2663
1	3471	2411
2	5001	2406

prune467.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
0.3b	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
0.3b	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
68×	`add-exp-log` `add-cbrt-cube`
67×	`pow-prod-down`
34×	`prod-exp` `cbrt-unprod`
28×	`times-frac`
25×	`flip3--` `flip--`
24×	`associate-/r/`
20×	`add-sqr-sqrt` `associate-/l*`
18×	`*-un-lft-identity`
16×	`frac-times`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`associate-r/` `associate-l` `associate-l/`
6×	`prod-diff` `difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-plus` `div-sub` `associate-/l/`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/r` `-commutative` `distribute-lft-out--`
1×	`pow2` `distribute-rgt-neg-in` `sub0-neg` `swap-sqr` `sqrt-prod` `distribute-rgt-neg-out` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

32.0ms	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
24.0ms	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
29.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
121.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
187.0ms	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
36.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	975	3538
1	5001	2962

prune586.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* 2.0 a) (/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))))
0.3b	(/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
0.3b	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
121×	`pow1`
120×	`add-exp-log`
76×	`add-cbrt-cube`
67×	`pow-prod-down`
56×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
46×	`div-exp`
45×	`associate-/r/`
44×	`add-cube-cbrt` `prod-exp`
37×	`flip3--` `flip--`
34×	`cbrt-unprod`
24×	`frac-times`
22×	`associate-/r*`
19×	`cbrt-undiv`
12×	`associate-r/` `associate-l/`
10×	`div-inv`
9×	`pow-sqr` `pow-prod-up`
8×	`associate-l` `difference-of-squares`
7×	`rec-exp` `1-exp` `associate-/l*`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`pow-plus`
2×	`sub-neg` `frac-2neg` `sub0-neg` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out--`
1×	`pow2` `pow-flip` `distribute-rgt-neg-in` `div-sub` `distribute-frac-neg` `swap-sqr` `sqrt-prod` `distribute-rgt-neg-out` `inv-pow` `unswap-sqr`

Counts

4 → 272

Calls

4 calls:

42.0ms	(/ 1 (/ (* 2.0 a) (/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))))
21.0ms	(/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
51.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
29.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ 1 (/ (* 2.0 a) (/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))))
183.0ms	(/ (- 0 (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
121.0ms	(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
36.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1296	6080
1	5002	5414

prune742.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	20
1	46	20
2	57	20
3	57	20

end0.0ms

sample3.3s

Algorithm

intervals

Results

890.0ms	3685×	body	320	valid
725.0ms	8199×	body	80	nan
577.0ms	16199×	pre	80	true
498.0ms	2937×	body	160	valid
159.0ms	498×	body	640	valid
86.0ms	880×	body	80	valid