Details

sample312.0ms

Algorithm

intervals

Results

10.0ms	187×	body	80	valid
8.0ms	33×	body	2560	valid
6.0ms	32×	body	1280	valid
4.0ms	95×	body	80	nan
1.0ms	5×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

22.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify146.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune228.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	81	11	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 6.3b

Counts

93 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.5b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
219.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
260.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune455.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	221	8	229

Merged error: 6.3b

Counts

229 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.2b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.6b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
26.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
233.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
198.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune930.0ms

Filtered

503 candidates to 303 candidates (60.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	502	9	511

Merged error: 6.3b

Counts

511 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
10.5b	(* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
28×	`add-exp-log`
27×	`associate-r`
26×	`times-frac`
19×	`add-cube-cbrt`
18×	`add-cbrt-cube`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`associate-/l/`
5×	`cbrt-undiv`
4×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+`
3×	`flip3--` `associate-l` `associate-/r*` `flip--` `unswap-sqr`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l`

Counts

4 → 118

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
18.0ms	(* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
242.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
257.0ms	(* (+ 0 (* a c)) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify127.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	603	1363
1	3253	1140
2	5002	1105

prune260.0ms

Filtered

130 candidates to 91 candidates (70.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Merged error: 6.3b

Counts

139 → 9

regimes238.0ms

Accuracy

87.9% (3.1b remaining)

Error of 8.5b against oracle of 5.3b and baseline of 31.3b

bsearch119.0ms

Steps

Iters	Range	Point
4	2.4689314423018332e-42	4.020507772702371e-42	3.959492018232498e-42
9	1.0212146627450078e-278	3.602416220665975e-273	1.0339546735098675e-278
7	-3.119450221310465e+111	-1.7054991696093843e+109	-8.449278771600537e+109

Iters

Range

Point

2.4689314423018332e-42

4.020507772702371e-42

3.959492018232498e-42

1.0212146627450078e-278

3.602416220665975e-273

1.0339546735098675e-278

-3.119450221310465e+111

-1.7054991696093843e+109

-8.449278771600537e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

255.0ms	5868×	body	80	valid
250.0ms	1033×	body	2560	valid
181.0ms	909×	body	1280	valid
120.0ms	2893×	body	80	nan
72.0ms	457×	body	640	valid
35.0ms	119×	body	5120	valid
27.0ms	232×	body	320	valid
10.0ms	126×	body	160	valid

Details

sample312.0ms

simplify14.0ms

prune4.0ms

localize12.0ms

rewrite43.0ms

series302.0ms

simplify146.0ms

prune228.0ms

localize12.0ms

rewrite51.0ms

series624.0ms

simplify116.0ms

prune455.0ms

localize11.0ms

rewrite92.0ms

series568.0ms

simplify110.0ms

prune930.0ms

localize13.0ms

rewrite53.0ms

series629.0ms

simplify127.0ms

prune260.0ms

regimes238.0ms

bsearch119.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling