Details

sample55.0ms

Algorithm

intervals

Results

14.0ms	200×	body	80	valid
8.0ms	23×	body	1280	valid
7.0ms	21×	body	2560	valid
6.0ms	87×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

36.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune251.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
153.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
188.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune488.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.0b	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
119×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
70×	`add-cube-cbrt`
32×	`add-exp-log`
25×	`associate-/r*`
24×	`difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp`
15×	`sqrt-prod`
12×	`distribute-lft-out--`
10×	`cbrt-undiv`
6×	`prod-exp` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `associate-/r/` `associate-/l/`

Counts

4 → 162

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
18.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
164.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
129.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	773	2158
1	3591	1999
2	5002	1976

prune422.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

23.2b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
24.0b	(cbrt (- (* b_2 b_2) (* a c)))
24.0b	(cbrt (- (* b_2 b_2) (* a c)))
24.0b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

34.0ms	(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)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
86.0ms	(cbrt (- (* b_2 b_2) (* a c)))
105.0ms	(cbrt (- (* b_2 b_2) (* a c)))
86.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify177.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	338	1554
1	845	1512
2	3653	1494
3	5001	1427

prune288.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.0b

regimes226.0ms

Accuracy

87.4% (3.2b remaining)

Error of 9.0b against oracle of 5.8b and baseline of 31.4b

bsearch127.0ms

Steps

Iters	Range		Point
7	6.184155830638016e+27	1.3306260697673677e+30	1.1253137591959452e+30
9	9.640766105553656e-271	8.801855242554939e-263	6.325255702488268e-270
3	-5.857739979673282e+80	-4.162495233614184e+80	-4.862167828845928e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	44	24
2	44	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

412.0ms	5867×	body	80	valid
351.0ms	1040×	body	2560	valid
254.0ms	899×	body	1280	valid
188.0ms	2906×	body	80	nan
98.0ms	436×	body	640	valid
46.0ms	115×	body	5120	valid
43.0ms	258×	body	320	valid
15.0ms	128×	body	160	valid