Details

sample58.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
11.0ms	33×	body	2560	valid
8.0ms	30×	body	1280	valid
6.0ms	102×	body	80	nan
2.0ms	6×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

45.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940

prune890.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune957.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize15.0ms

Local error

Found 4 expressions with local error:

23.7b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
24.5b	(cbrt (- (* b_2 b_2) (* a c)))
24.5b	(cbrt (- (* b_2 b_2) (* a c)))
24.5b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

35.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))
3.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
22.0ms	(cbrt (- (* b_2 b_2) (* a c)))
22.0ms	(cbrt (- (* b_2 b_2) (* a c)))
25.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify183.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (169.0ms)

Iter	Nodes	Cost
0	352	1616
1	903	1574
2	3956	1556
3	5001	1553

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.8b

regimes478.0ms

Accuracy

82.6% (4.9b remaining)

Error of 10.8b against oracle of 5.9b and baseline of 33.9b

bsearch65.0ms

Steps

Iters	Range		Point
7	7.8930669794294e+68	1.794276654474529e+70	1.7701741483501238e+70
9	-1.8496456666423901e-16	-6.821017948976997e-23	-6.931537337855704e-23

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

367.0ms	1059×	body	2560	valid
341.0ms	5874×	body	80	valid
257.0ms	884×	body	1280	valid
157.0ms	2865×	body	80	nan
103.0ms	448×	body	640	valid
49.0ms	117×	body	5120	valid
35.0ms	208×	body	320	valid
14.0ms	126×	body	160	valid