Details

sample69.0ms

Algorithm

intervals

Results

16.0ms	188×	body	80	valid
13.0ms	31×	body	1280	valid
12.0ms	30×	body	2560	valid
8.0ms	91×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	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: 33.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite56.0ms

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	(- (* b b) (* (* 3.0 a) c))
37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune216.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
27.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
177.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify124.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.2b	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
10.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r` `associate-/r*`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
26.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series681.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
350.0ms	(* (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
183.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify146.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (126.0ms)

Iter	Nodes	Cost
0	739	2415
1	3893	2081
2	5001	2074

prune402.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
44.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	307	470
1	1303	428
2	5001	417

prune157.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

regimes189.0ms

Accuracy

83.6% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 33.0b

bsearch123.0ms

Steps

Iters	Range		Point
8	2.3682374127768157e-71	9.144612143045527e-68	1.1752867948836086e-69
7	-1.2511146020293208e+129	-2.5570389401985865e+127	-4.032376794487168e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample2.0s

Algorithm

intervals

Results

538.0ms	5911×	body	80	valid
439.0ms	1057×	body	2560	valid
294.0ms	846×	body	1280	valid
241.0ms	2844×	body	80	nan
131.0ms	459×	body	640	valid
48.0ms	226×	body	320	valid
46.0ms	93×	body	5120	valid
19.0ms	128×	body	160	valid