Details

sample64.0ms

Algorithm

intervals

Results

12.0ms	102×	body	320	valid
11.0ms	277×	body	80	nan
10.0ms	533×	pre	80	true
9.0ms	106×	body	160	valid
2.0ms	14×	body	640	valid
1.0ms	34×	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: 50.1b

localize17.0ms

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))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite110.0ms

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:

9.0ms	(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))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(- (* b b) (* (* 4.0 a) c))
97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune329.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `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 → 151

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
90.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series410.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
165.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
134.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify111.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5002	2388

prune925.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.4b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
52×	`add-exp-log`
45×	`times-frac`
32×	`add-cbrt-cube`
28×	`add-cube-cbrt`
27×	`associate-r`
18×	`div-exp`
17×	`prod-exp`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
8×	`distribute-rgt-neg-in` `associate-/r*` `sqrt-prod` `add-log-exp`
7×	`pow1`
6×	`associate-/l/`
4×	`frac-times` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `flip-+` `associate-/l`
3×	`flip3--` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow-flip` `pow-prod-down` `neg-log` `*-commutative` `inv-pow`

Counts

4 → 156

Calls

4 calls:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
41.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
102.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
136.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
166.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify168.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (149.0ms)

Iter	Nodes	Cost
0	710	2295
1	4363	1911
2	5002	1887

prune907.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b	(* (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ 1 (* 2.0 a)))
0.4b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-exp-log`
82×	`prod-exp`
69×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
47×	`times-frac` `add-cbrt-cube`
38×	`div-exp`
34×	`associate-r`
30×	`add-cube-cbrt`
20×	`cbrt-unprod`
19×	`rec-exp` `1-exp`
16×	`distribute-lft-out--` `difference-of-squares`
12×	`pow1` `frac-times` `associate-*l/`
11×	`cbrt-undiv`
8×	`distribute-rgt-neg-in` `sqrt-prod` `add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l*` `pow-prod-down` `associate-/r/` `un-div-inv`
3×	`flip3--` `flip--` `div-inv` `associate-/l*` `unswap-sqr`
2×	`diff-log` `*-commutative`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow-flip` `frac-2neg` `neg-log` `clear-num` `inv-pow`

Counts

4 → 197

Calls

4 calls:

23.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
138.0ms	(* (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ 1 (* 2.0 a)))
102.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
131.0ms	(* (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (/ 1 (* 2.0 a)))
162.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	919	3021
1	5001	2437

prune798.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	33	14
2	33	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

434.0ms	3620×	body	320	valid
312.0ms	15998×	pre	80	true
309.0ms	7998×	body	80	nan
237.0ms	2945×	body	160	valid
83.0ms	523×	body	640	valid
37.0ms	912×	body	80	valid