Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	109×	body	320	valid
9.0ms	498×	pre	80	true
8.0ms	242×	body	80	nan
7.0ms	111×	body	160	valid
2.0ms	15×	body	640	valid
1.0ms	21×	body	80	valid

simplify13.0ms

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: 53.9b

localize10.0ms

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)
27.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite58.0ms

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:

2.0ms	(- (* b b) (* (* 3.0 a) c))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
105.0ms	(/ (+ (- 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))))

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

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

prune164.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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

rewrite363.0ms

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:

6.0ms	(* (* 3.0 a) c)
6.0ms	(* 3.0 (* a c))
163.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
181.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series337.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
20.0ms	(* 3.0 (* a c))
167.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
130.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify118.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (90.0ms)

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

prune432.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
136×	`add-sqr-sqrt`
121×	`*-un-lft-identity`
113×	`add-exp-log`
73×	`add-cbrt-cube`
59×	`add-cube-cbrt` `associate-r`
45×	`div-exp`
41×	`prod-exp`
30×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-undiv`
25×	`cbrt-unprod`
18×	`div-inv`
17×	`associate-l`
16×	`pow1`
15×	`distribute-rgt-neg-in` `sqrt-prod`
7×	`pow-prod-down` `associate-/r` `associate-/l`
6×	`unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`associate-/r/` `add-log-exp`
3×	`*-commutative`
2×	`flip3--` `flip--`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`

Counts

4 → 236

Calls

4 calls:

29.0ms	(/ (/ (* 3.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* (* 3.0 a) c)
6.0ms	(* 3.0 (* a c))
80.0ms	(* (/ 1 3.0) (/ (/ (* 3.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (/ (* 3.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* (* 3.0 a) c)
20.0ms	(* 3.0 (* a c))
155.0ms	(* (/ 1 3.0) (/ (/ (* 3.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1023	3615
1	5001	3062

prune511.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
90×	`times-frac`
85×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
74×	`pow-prod-down`
60×	`sqrt-pow1`
43×	`add-cube-cbrt`
30×	`associate-/l*`
25×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
17×	`pow-prod-up`
14×	`sqrt-prod`
12×	`pow1/2`
11×	`pow-sqr`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`prod-exp` `associate-/r/` `cbrt-unprod`
5×	`associate-l`
4×	`swap-sqr` `div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `clear-num` `*-commutative`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `flip-+` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
165.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
181.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
37.0ms	(* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
391.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
321.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
81.0ms	(* (sqrt (* (* 3.0 a) c)) (sqrt (* (* 3.0 a) c)))

simplify166.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	725	4126
1	4247	3189
2	5002	3142

prune466.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes139.0ms

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	24	16
1	24	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

347.0ms	3606×	body	320	valid
303.0ms	16228×	pre	80	true
259.0ms	8228×	body	80	nan
193.0ms	2994×	body	160	valid
61.0ms	477×	body	640	valid
30.0ms	923×	body	80	valid