Details

sample60.0ms

Algorithm

intervals

Results

13.0ms	128×	body	320	valid
10.0ms	536×	pre	80	true
9.0ms	280×	body	80	nan
6.0ms	90×	body	160	valid
4.0ms	11×	body	640	valid
1.0ms	27×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 53.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 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)
26.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite30.0ms

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))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
5.0ms	(* (* 3.0 a) c)
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
19.0ms	(* (* 3.0 a) c)
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (47.0ms)

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

prune168.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

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:

5.0ms	(* (* 3.0 a) c)
5.0ms	(* 3.0 (* a c))
32.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
26.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
19.0ms	(* 3.0 (* a c))
124.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
169.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (91.0ms)

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

prune430.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 159

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
5.0ms	(* (* 3.0 a) c)
29.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
30.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
19.0ms	(* (* 3.0 a) c)
129.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
166.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	627	3101
1	3139	2568
2	5001	2534

prune398.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(/ (* 3.0 (* a c)) 3.0)
0.3b	(* 3.0 (* a c))
0.4b	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

155×	`times-frac`
119×	`add-sqr-sqrt`
113×	`add-exp-log`
108×	`*-un-lft-identity`
89×	`associate-r`
77×	`add-cbrt-cube`
71×	`add-cube-cbrt`
44×	`prod-exp`
42×	`div-exp`
30×	`cbrt-unprod`
24×	`cbrt-undiv`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
11×	`associate-l`
9×	`distribute-rgt-neg-in` `sqrt-prod`
7×	`pow-prod-down`
6×	`associate-/r/` `div-inv`
4×	`rec-exp` `1-exp` `add-log-exp` `unswap-sqr`
3×	`flip3--` `associate-/r` `-commutative` `flip--`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l*`

Counts

4 → 199

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
6.0ms	(/ (* 3.0 (* a c)) 3.0)
5.0ms	(* 3.0 (* a c))
42.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series213.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
19.0ms	(/ (* 3.0 (* a c)) 3.0)
19.0ms	(* 3.0 (* a c))
150.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify49.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1119	2646
1	5001	2153

prune431.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

376.0ms	3711×	body	320	valid
316.0ms	16302×	pre	80	true
261.0ms	8302×	body	80	nan
198.0ms	2943×	body	160	valid
65.0ms	476×	body	640	valid
29.0ms	870×	body	80	valid