Details

sample285.0ms

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
3.0ms	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	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	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

localize11.0ms

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)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (* 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))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune276.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 6.3b

Counts

113 → 9

localize11.0ms

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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
21×	`distribute-lft-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
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 → 284

Calls

4 calls:

10.0ms	(- (- 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)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
137.0ms	(/ (/ (+ 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)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify145.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505

prune534.0ms

Filtered

296 candidates to 172 candidates (58.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	294	2	296
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	297	8	305

Merged error: 6.2b

Counts

305 → 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)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
630×	`add-sqr-sqrt`
629×	`*-un-lft-identity`
433×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
82×	`sqrt-prod`
70×	`distribute-rgt-neg-in`
60×	`prod-diff`
28×	`associate-/r*`
22×	`div-inv`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 569

Calls

4 calls:

17.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
27.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
160.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify130.0ms

Algorithm

egg-herbie

Counts

581 → 581

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1755	10832
1	5002	9428

prune1.1s

Filtered

581 candidates to 328 candidates (56.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	579	2	581
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	580	9	589

Merged error: 6.2b

Counts

589 → 9

localize19.0ms

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)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

891×	`times-frac`
641×	`add-sqr-sqrt`
566×	`*-un-lft-identity`
418×	`add-cube-cbrt`
140×	`log-prod` `exp-sum`
111×	`difference-of-squares`
90×	`prod-diff`
89×	`associate-/l*`
74×	`distribute-lft-out--`
73×	`sqrt-prod`
67×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
17×	`div-inv`
13×	`add-exp-log` `add-cbrt-cube`
10×	`neg-mul-1` `fma-neg`
8×	`add-log-exp`
7×	`pow1`
6×	`cbrt-undiv` `exp-prod` `div-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u`
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 → 540

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)
13.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
151.0ms	(/ (/ a (/ (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
71.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify133.0ms

Algorithm

egg-herbie

Counts

552 → 552

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2050	12892
1	5002	10123

prune1.1s

Filtered

552 candidates to 298 candidates (54.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	550	2	552
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	552	9	561

Merged error: 6.2b

Counts

561 → 9

regimes210.0ms

Accuracy

90.5% (2.5b remaining)

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

bsearch145.0ms

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

260.0ms	5874×	body	80	valid
256.0ms	1055×	body	2560	valid
179.0ms	901×	body	1280	valid
118.0ms	2908×	body	80	nan
67.0ms	430×	body	640	valid
30.0ms	101×	body	5120	valid
28.0ms	238×	body	320	valid
9.0ms	109×	body	160	valid