Details

sample66.0ms

Algorithm

intervals

Results

14.0ms	126×	body	320	valid
13.0ms	280×	body	80	nan
10.0ms	536×	pre	80	true
7.0ms	91×	body	160	valid
2.0ms	11×	body	640	valid
1.0ms	28×	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: 53.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
26.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite32.0ms

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:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune242.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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))
0.2b	(/ (/ (+ 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)))))

rewrite43.0ms

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)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
153.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (103.0ms)

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

prune457.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

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))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
28×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`sqrt-prod` `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 → 118

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms	(- (* b b) (* (* 4.0 a) c))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt 1) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify117.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	652	2171
1	3418	1893
2	5001	1888

prune473.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

665×	`times-frac`
530×	`add-sqr-sqrt`
482×	`*-un-lft-identity`
286×	`add-cube-cbrt`
239×	`sqrt-prod`
148×	`associate-r`
98×	`distribute-lft-out--` `difference-of-squares`
54×	`associate-/l*`
49×	`distribute-rgt-neg-in`
32×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l`
16×	`associate-/r/`
13×	`cbrt-undiv` `div-exp`
12×	`unswap-sqr`
11×	`div-inv`
10×	`associate-/r*`
8×	`flip3--` `flip--`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 510

Calls

4 calls:

3.0ms	(sqrt (+ 0 (* 4.0 (* a c))))
21.0ms	(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
13.0ms	(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms	(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series1.4s

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (+ 0 (* 4.0 (* a c))))
407.0ms	(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
410.0ms	(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
412.0ms	(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify125.0ms

Algorithm

egg-herbie

Counts

522 → 522

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1572	11350
1	5001	10801

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	15
1	32	15
2	32	15

end0.0ms

sample1.7s

Algorithm

intervals

Results

412.0ms	3716×	body	320	valid
303.0ms	16332×	pre	80	true
296.0ms	8332×	body	80	nan
214.0ms	2939×	body	160	valid
72.0ms	474×	body	640	valid
32.0ms	871×	body	80	valid