Details

sample62.0ms

Algorithm

intervals

Results

13.0ms	123×	body	320	valid
11.0ms	520×	pre	80	true
9.0ms	264×	body	80	nan
8.0ms	85×	body	160	valid
2.0ms	16×	body	640	valid
1.0ms	32×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
25.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 73

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(* (* 3.0 a) c)
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
20.0ms	(* (* 3.0 a) c)
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	419	716
1	1930	613
2	5002	608

prune176.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* (* 3.0 a) c)
0.3b	(* 3.0 (* a c))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`associate-r` `associate-l` `div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 159

Calls

4 calls:

166.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* (* 3.0 a) c)
6.0ms	(* 3.0 (* a c))
184.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series333.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms	(* (* 3.0 a) c)
19.0ms	(* 3.0 (* a c))
128.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify121.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	684	3100
1	3307	2567
2	5001	2533

prune438.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
0.3b	(* (* 3.0 a) c)
0.3b	(* 3.0 (* a c))
0.3b	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

317×	`times-frac`
237×	`add-sqr-sqrt`
226×	`*-un-lft-identity`
141×	`add-cube-cbrt`
113×	`add-exp-log`
89×	`associate-r`
73×	`add-cbrt-cube`
45×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
41×	`prod-exp`
27×	`cbrt-unprod` `associate-/l*`
24×	`cbrt-undiv`
21×	`distribute-rgt-neg-in` `sqrt-prod`
16×	`pow1`
14×	`associate-/r/`
11×	`associate-l`
10×	`div-inv`
7×	`flip3--` `pow-prod-down` `flip--`
5×	`rec-exp` `1-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/r` `-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`

Counts

4 → 304

Calls

4 calls:

39.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
6.0ms	(* (* 3.0 a) c)
6.0ms	(* 3.0 (* a c))
93.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series316.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
23.0ms	(* (* 3.0 a) c)
19.0ms	(* 3.0 (* a c))
152.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify70.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1286	4850
1	5002	4259

prune663.0ms

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	(* (* 3.0 a) c)
0.3b	(/ 1 (* 3.0 a))
0.3b	(* 3.0 (* a c))
0.3b	(* (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
40×	`add-cbrt-cube`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`associate-l`
29×	`prod-exp`
28×	`times-frac`
21×	`add-cube-cbrt`
19×	`pow1` `div-exp`
15×	`cbrt-unprod`
11×	`associate-r`
9×	`cbrt-undiv`
8×	`pow-prod-down`
6×	`rec-exp` `1-exp` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`distribute-rgt-neg-in` `sqrt-prod` `-commutative` `div-inv` `associate-/l`
2×	`pow-flip` `associate-/r/` `unswap-sqr`
1×	`frac-times` `flip3--` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*` `un-div-inv` `flip--` `inv-pow`

Counts

4 → 133

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
4.0ms	(/ 1 (* 3.0 a))
6.0ms	(* 3.0 (* a c))
239.0ms	(* (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
16.0ms	(/ 1 (* 3.0 a))
19.0ms	(* 3.0 (* a c))
131.0ms	(* (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))

simplify102.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	626	1711
1	3343	1287
2	5001	1236

prune312.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes149.0ms

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	25	13
1	25	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

371.0ms	3587×	body	320	valid
337.0ms	16201×	pre	80	true
278.0ms	8201×	body	80	nan
211.0ms	3049×	body	160	valid
70.0ms	503×	body	640	valid
31.0ms	861×	body	80	valid