Details

analyze961.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

sample33.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5321	37

prune11.0ms

Filtered

1 candidates to 1 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: 25.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 2.0) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
24.2b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `div-exp` `associate-*l/` `flip--` `div-inv` `associate-/l/`
1×	`frac-2neg` `clear-num` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

29.0ms	(* (- x 2.0) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
12.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
26.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series87.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- x 2.0) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
35.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify63.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5010	3664

prune323.0ms

Filtered

95 candidates to 127 candidates (-33.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	123	6	129

Merged error: 0.0b

Counts

129 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 2.0) (/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.2b	(/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)))
24.2b	(/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
114×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
53×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`associate-/r*` `associate-/r/`
15×	`div-exp`
10×	`flip3-+` `flip-+` `div-inv`
9×	`pow1`
8×	`associate-l` `prod-exp`
7×	`cbrt-undiv`
6×	`associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-*r/`
2×	`frac-times` `flip3--` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `un-div-inv` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 222

Calls

4 calls:

38.0ms	(* (- x 2.0) (/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))))
9.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
25.0ms	(/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)))
26.0ms	(/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

series114.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (- x 2.0) (/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
38.0ms	(/ 1 (/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)))
32.0ms	(/ (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

simplify103.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4976	9717
1	4976	9717

prune722.0ms

Filtered

159 candidates to 234 candidates (-47.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	233	7	240

Merged error: 0.0b

Counts

240 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
6.4b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
17.5b	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
20.9b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
53.0ms	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
36.0ms	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
54.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify310.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4960	7444
1	4960	7444

prune547.0ms

Filtered

111 candidates to 172 candidates (-55.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	172	7	179

Merged error: 0.0b

Counts

179 → 7

localize41.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
14.7b	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
14.7b	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
14.7b	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

15.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
13.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
13.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

series108.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
34.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
32.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
32.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))

simplify71.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5333	1718

prune339.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

regimes345.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.9b

bsearch24.0ms

Steps

Iters	Range		Point
0	4.464099250270867e+27	4.615315716884081e+27	4.539707483577474e+27
9	-6.839233690354166e+36	-3.8394254712486548e+31	-3.19180493211719e+35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	59
1	80	59

end0.0ms

sample827.0ms

Algorithm

intervals

Results

649.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze961.0ms

sample33.0ms

simplify37.0ms

prune11.0ms

localize24.0ms

rewrite76.0ms

series87.0ms

simplify63.0ms

prune323.0ms

localize25.0ms

rewrite107.0ms

series114.0ms

simplify103.0ms

prune722.0ms

localize30.0ms

rewrite111.0ms

series102.0ms

simplify310.0ms

prune547.0ms

localize41.0ms

rewrite54.0ms

series108.0ms

simplify71.0ms

prune339.0ms

regimes345.0ms

bsearch24.0ms

simplify2.0ms

end0.0ms

sample827.0ms

Profiling