Details

sample62.0ms

Algorithm

intervals

Results

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

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize11.0ms

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))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))))

rewrite42.0ms

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×	`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` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* 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)))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(/ (/ (+ 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)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	640	2579
1	3157	2332
2	5001	2319

prune406.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))
0.1b	(+ (* b b) (- 0 (* 4.0 (* a c))))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))

rewrite50.0ms

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`
9×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`div-inv`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/`
2×	`associate-+r+` `frac-2neg` `sub0-neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `unsub-neg`

Counts

4 → 153

Calls

4 calls:

5.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))
5.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))
46.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	646	2793
1	3132	2522
2	5003	2507

prune410.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

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

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

810×	`times-frac`
638×	`add-sqr-sqrt`
539×	`*-un-lft-identity`
335×	`add-cube-cbrt`
264×	`sqrt-prod`
148×	`associate-r`
98×	`distribute-lft-out--` `difference-of-squares`
70×	`associate-l`
59×	`add-exp-log`
54×	`associate-/l*`
49×	`distribute-rgt-neg-in`
47×	`add-cbrt-cube`
31×	`div-exp`
24×	`unswap-sqr`
22×	`cbrt-undiv`
16×	`associate-/r/`
14×	`div-inv`
12×	`prod-exp`
10×	`associate-/r*`
9×	`cbrt-unprod`
8×	`flip3--` `flip--`
7×	`pow1`
4×	`sqrt-div` `add-log-exp`
3×	`1-exp` `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 → 571

Calls

4 calls:

3.0ms	(sqrt (+ 0 (* 4.0 (* a c))))
21.0ms	(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) a)
14.0ms	(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
156.0ms	(* (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) 1) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) a))

series1.3s

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (+ 0 (* 4.0 (* a c))))
408.0ms	(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) a)
395.0ms	(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
414.0ms	(* (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) 1) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) a))

simplify151.0ms

Algorithm

egg-herbie

Counts

583 → 583

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1931	14056
1	5001	13400

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes84.0ms

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	24	14
1	36	14
2	42	14
3	42	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

422.0ms	3716×	body	320	valid
306.0ms	16332×	pre	80	true
301.0ms	8332×	body	80	nan
221.0ms	2939×	body	160	valid
71.0ms	474×	body	640	valid
34.0ms	871×	body	80	valid