Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
6.0ms	181×	body	80	valid
6.0ms	36×	body	1280	valid
3.0ms	99×	body	80	nan
3.0ms	21×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b	(- (* b b) (* (* 3.0 a) c))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

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)
7.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

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))
66.0ms	(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

prune184.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.5b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite50.0ms

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:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (+ 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)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- 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)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (90.0ms)

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

prune431.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.4b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
10.5b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
141.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
184.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	702	2050
1	4419	1582
2	5002	1541

prune374.0ms

Filtered

128 candidates to 86 candidates (67.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.4b	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
10.5b	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `sqrt-prod` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
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` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 136

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
13.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
171.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	619	2073
1	2889	1850
2	5001	1834

prune408.0ms

Filtered

148 candidates to 103 candidates (69.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.7b

regimes410.0ms

Accuracy

83.2% (3.8b remaining)

Error of 13.0b against oracle of 9.2b and baseline of 31.8b

bsearch153.0ms

Steps

Iters	Range		Point
9	3.165357225717215e+147	1.0059809584366412e+156	1.1782587992148885e+154
7	-1.6140014456430585e-244	-6.375027159262035e-246	-2.0878089492086545e-245
7	-21754618.13974568	-390992.43068670365	-21374171.270308975

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	49
1	48	49

end0.0ms

sample1.1s

Algorithm

intervals

Results

242.0ms	1141×	body	2560	valid
220.0ms	5762×	body	80	valid
163.0ms	939×	body	1280	valid
100.0ms	2987×	body	80	nan
62.0ms	466×	body	640	valid
23.0ms	90×	body	5120	valid
23.0ms	230×	body	320	valid
7.0ms	109×	body	160	valid