Details

sample286.0ms

Algorithm

intervals

Results

9.0ms	180×	body	80	valid
8.0ms	42×	body	1280	valid
7.0ms	28×	body	2560	valid
4.0ms	95×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

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

prune6.0ms

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	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune395.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 5.7b

Counts

104 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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))
16.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
193.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
243.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune722.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Merged error: 5.6b

Counts

206 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.5b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.9b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
26.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
212.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
167.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune1.4s

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	447	2	449
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	449	8	457

Merged error: 5.6b

Counts

457 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

21.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1746	7647
1	5002	6938

prune833.0ms

Filtered

435 candidates to 172 candidates (39.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	435	0	435
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	435	8	443

Merged error: 5.6b

Counts

443 → 8

regimes303.0ms

Accuracy

94.1% (1.4b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.5b

bsearch158.0ms

Steps

Iters	Range		Point
9	2.3323746097403884e+36	1.0155011232908699e+43	5.709720606171686e+42
8	1.0864170100501208e-268	1.947837268970173e-265	1.2011604238594458e-268
8	-1.66941495381885e+82	-1.0885129797411899e+78	-1.5096837178516531e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

254.0ms	1053×	body	2560	valid
241.0ms	5825×	body	80	valid
185.0ms	931×	body	1280	valid
113.0ms	2913×	body	80	nan
74.0ms	472×	body	640	valid
42.0ms	132×	body	5120	valid
23.0ms	196×	body	320	valid
10.0ms	128×	body	160	valid

Details

sample286.0ms

simplify12.0ms

prune6.0ms

localize12.0ms

rewrite46.0ms

series267.0ms

simplify41.0ms

prune395.0ms

localize11.0ms

rewrite45.0ms

series532.0ms

simplify102.0ms

prune722.0ms

localize10.0ms

rewrite81.0ms

series471.0ms

simplify96.0ms

prune1.4s

localize10.0ms

rewrite66.0ms

series274.0ms

simplify101.0ms

prune833.0ms

regimes303.0ms

bsearch158.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling