Details

sample76.0ms

Algorithm

intervals

Results

17.0ms	193×	body	80	valid
15.0ms	33×	body	2560	valid
11.0ms	30×	body	1280	valid
7.0ms	102×	body	80	nan
3.0ms	6×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

34.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune689.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

38.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	678	2536
1	2558	2441
2	5001	2441

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

55.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune701.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
471×	`add-sqr-sqrt`
470×	`*-un-lft-identity`
322×	`add-cube-cbrt`
80×	`associate-/r*`
74×	`distribute-lft-out--` `difference-of-squares`
40×	`sqrt-prod`
37×	`distribute-rgt-neg-in`
25×	`add-exp-log`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
10×	`add-log-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
3×	`rec-exp` `flip3--` `diff-log` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 393

Calls

4 calls:

39.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify88.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1362	7523
1	5001	7036

prune2.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes354.0ms

Accuracy

87.3% (3.6b remaining)

Error of 9.3b against oracle of 5.8b and baseline of 34.0b

bsearch111.0ms

Steps

Iters	Range		Point
7	7.8930669794294e+68	1.794276654474529e+70	1.3845340503596435e+70
9	-1.1004795362994629e-128	-8.053772428904448e-138	-1.461539579389551e-137
6	-16116865.97641067	-1132915.5505216778	-14858297.008745154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

490.0ms	1060×	body	2560	valid
452.0ms	5878×	body	80	valid
337.0ms	884×	body	1280	valid
212.0ms	2868×	body	80	nan
131.0ms	444×	body	640	valid
69.0ms	116×	body	5120	valid
46.0ms	209×	body	320	valid
19.0ms	125×	body	160	valid