Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	30×	body	2560	valid
4.0ms	25×	body	1280	valid
3.0ms	99×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	5×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

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:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
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)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
50.0ms	(- (* 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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

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

prune233.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.2b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite86.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
46.0ms	(/ (/ (+ 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)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
155.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
181.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (92.0ms)

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

prune419.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.2b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
18.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
155.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
181.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	682	1938
1	4416	1476
2	5002	1435

prune298.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
3.4b	(/ (/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
11.2b	(/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
115×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
62×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
48×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/` `associate-/r/` `distribute-neg-frac`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod`
2×	`neg-sub0` `frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 279

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
5.0ms	(/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
179.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
223.0ms	(/ (- (* (* 3.0 a) c)) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1268	5558
1	5001	5359

prune957.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

regimes387.0ms

Accuracy

87.8% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 31.7b

bsearch277.0ms

Steps

Iters	Range		Point
7	6.714891876596302e+121	1.686395921989292e+123	7.690556826815447e+121
6	2.4634856426385367e+30	1.375897298344625e+31	2.4873867190524188e+30
11	1.7382738099505427e-22	0.7032085127721847	9.817283457339674e-08
8	-1.4984247517127078e-204	-1.6903052606039677e-207	-1.7200956384996044e-207
8	-2.1136969993533704e+133	-9.628024177185589e+129	-2.1419401754731713e+130

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	56
1	66	56
2	69	56
3	69	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

226.0ms	1083×	body	2560	valid
212.0ms	5893×	body	80	valid
154.0ms	895×	body	1280	valid
94.0ms	2933×	body	80	nan
57.0ms	440×	body	640	valid
32.0ms	117×	body	5120	valid
22.0ms	227×	body	320	valid
6.0ms	98×	body	160	valid