Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	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: 34.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

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:

5.0ms	(* (* 3.0 a) c)
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune183.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.7b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.4b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
148.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
184.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune424.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
12.1b	(/ (* 3.0 a) (* 3.0 (* a c)))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	417	636
1	2439	522
2	5001	492

prune239.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 1) (* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.1b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

259×	`add-exp-log`
205×	`div-exp`
97×	`1-exp`
70×	`prod-exp`
43×	`rec-exp`
36×	`add-cbrt-cube`
31×	`times-frac`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-undiv`
13×	`associate-/l*`
10×	`add-log-exp`
6×	`cbrt-unprod`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 173

Calls

4 calls:

21.0ms	(/ (/ 1 1) (* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (/ 1 1) (* (/ 1 (/ c 1)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1018	2122
1	3933	1685
2	5001	1646

prune278.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.7b

regimes381.0ms

Accuracy

81.6% (4.0b remaining)

Error of 11.2b against oracle of 7.2b and baseline of 28.9b

bsearch170.0ms

Steps

Iters	Range		Point
6	1.0219281492460531e+154	1.0045197732059615e+155	1.3695280426588302e+154
9	-3.690646844280796e-57	-1.3984745828373551e-64	-1.4167290353563065e-64
8	-183484304836700.72	-121429039431.98735	-34801737241079.82

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	45
1	66	45
2	66	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	1081×	body	2560	valid
221.0ms	5782×	body	80	valid
174.0ms	927×	body	1280	valid
110.0ms	2977×	body	80	nan
66.0ms	451×	body	640	valid
30.0ms	104×	body	5120	valid
27.0ms	257×	body	320	valid
9.0ms	124×	body	160	valid