Details

sample285.0ms

Algorithm

intervals

Results

9.0ms	205×	body	80	valid
6.0ms	26×	body	2560	valid
5.0ms	75×	body	80	nan
5.0ms	25×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid

simplify15.0ms

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: 32.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.4b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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:

23.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune218.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 6.0b

Counts

93 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.4b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	448	823
1	1968	724
2	5003	682

prune197.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Merged error: 6.0b

Counts

106 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

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:

20.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
163.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune445.0ms

Filtered

218 candidates to 146 candidates (67.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	217	9	226

Merged error: 6.0b

Counts

226 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.8b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

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:

30.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
176.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1582	8734
1	5001	8085

prune918.0ms

Filtered

503 candidates to 303 candidates (60.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	504	8	512

Merged error: 6.0b

Counts

512 → 8

regimes193.0ms

Accuracy

92.3% (1.9b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 30.1b

bsearch143.0ms

Steps

Iters	Range	Point
8	4.5418805312590315e+84	1.9690305180656607e+89	1.854315912301685e+89
6	-1.516458467021275e-303	-1.3767648779983776e-304	-1.4521535344124743e-304
8	-3.9548743960166396e+41	-6.269021281919223e+37	-3.868707050613547e+41

Iters

Range

Point

4.5418805312590315e+84

1.9690305180656607e+89

1.854315912301685e+89

-1.516458467021275e-303

-1.3767648779983776e-304

-1.4521535344124743e-304

-3.9548743960166396e+41

-6.269021281919223e+37

-3.868707050613547e+41

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	28
1	46	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

266.0ms	5891×	body	80	valid
265.0ms	1057×	body	2560	valid
184.0ms	873×	body	1280	valid
121.0ms	2906×	body	80	nan
75.0ms	451×	body	640	valid
35.0ms	108×	body	5120	valid
27.0ms	228×	body	320	valid
9.0ms	112×	body	160	valid

Details

sample285.0ms

simplify15.0ms

prune4.0ms

localize12.0ms

rewrite44.0ms

series270.0ms

simplify43.0ms

prune218.0ms

localize10.0ms

rewrite33.0ms

series248.0ms

simplify54.0ms

prune197.0ms

localize12.0ms

rewrite55.0ms

series424.0ms

simplify116.0ms

prune445.0ms

localize12.0ms

rewrite94.0ms

series463.0ms

simplify109.0ms

prune918.0ms

regimes193.0ms

bsearch143.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling