Details

sample287.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
8.0ms	181×	body	80	valid
6.0ms	101×	body	80	nan
6.0ms	27×	body	1280	valid
4.0ms	22×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	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: 35.7b

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)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b	(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:

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)
35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune231.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 6.3b

Counts

93 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
136.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
167.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

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

prune471.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	219	8	227

Merged error: 6.2b

Counts

227 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:

14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
149.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1582	8735
1	5001	8087

prune1000.0ms

Filtered

503 candidates to 304 candidates (60.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	502	9	511

Merged error: 6.2b

Counts

511 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

5.6b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
6.1b	(/ (/ a (/ (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
15.5b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

891×	`times-frac`
581×	`add-sqr-sqrt`
506×	`*-un-lft-identity`
358×	`add-cube-cbrt`
111×	`difference-of-squares`
89×	`associate-/l*`
80×	`log-prod` `exp-sum`
74×	`distribute-lft-out--`
43×	`sqrt-prod`
37×	`distribute-rgt-neg-in`
17×	`div-inv`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`cbrt-undiv` `exp-prod` `div-exp`
4×	`sqrt-div` `associate-/r/`
3×	`flip3--` `associate-/r*` `log-pow` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `neg-log` `clear-num` `rem-exp-log` `associate-/l/`

Counts

4 → 432

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
29.0ms	(/ (/ a (/ (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
10.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
146.0ms	(/ (/ a (/ (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
69.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

444 → 444

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1791	9016
1	5002	7992

prune985.0ms

Filtered

444 candidates to 256 candidates (57.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	442	2	444
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	444	9	453

Merged error: 6.2b

Counts

453 → 9

regimes211.0ms

Accuracy

90.5% (2.5b remaining)

Error of 8.5b against oracle of 5.9b and baseline of 32.3b

bsearch146.0ms

Steps

Iters	Range	Point
6	6.333441064762502e+69	2.6854631551896503e+70	1.4793880051580374e+70
10	-1.2256122484874663e-236	-9.129152522006918e-253	-9.271872778047194e-253
8	-1.666412824726956e+124	-3.415589734864014e+119	-5.377788818048344e+121

Iters

Range

Point

6.333441064762502e+69

2.6854631551896503e+70

1.4793880051580374e+70

-1.2256122484874663e-236

-9.129152522006918e-253

-9.271872778047194e-253

-1.666412824726956e+124

-3.415589734864014e+119

-5.377788818048344e+121

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

265.0ms	5874×	body	80	valid
260.0ms	1055×	body	2560	valid
181.0ms	901×	body	1280	valid
122.0ms	2908×	body	80	nan
70.0ms	430×	body	640	valid
35.0ms	101×	body	5120	valid
28.0ms	238×	body	320	valid
9.0ms	109×	body	160	valid