Details

analyze979.0ms

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

sample31.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

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

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
0.1b	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
24.1b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
6×	`associate-*r/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 97

Calls

4 calls:

7.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
10.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
13.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series58.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
11.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
37.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify48.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4994	2437
1	4994	2437

prune242.0ms

Filtered

78 candidates to 109 candidates (-39.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Merged error: 0.0b

Counts

111 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* 78.6994924154 78.6994924154))
0.5b	(- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154)))
4.9b	(/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154))
24.1b	(/ (+ (* x (+ (* x (+ (/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/` `associate-/l/`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`sub-neg` `diff-log` `div-sub` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

5.0ms	(* x (* 78.6994924154 78.6994924154))
7.0ms	(- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154)))
12.0ms	(/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154))
33.0ms	(/ (+ (* x (+ (* x (+ (/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series66.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* x (* 78.6994924154 78.6994924154))
9.0ms	(- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154)))
7.0ms	(/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154))
49.0ms	(/ (+ (* x (+ (* x (+ (/ (- (* (pow x 3) (* 4.16438922228 4.16438922228)) (* x (* 78.6994924154 78.6994924154))) (- (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify39.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	6036	3242

prune323.0ms

Filtered

80 candidates to 105 candidates (-31.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	105	7	112

Merged error: 0.0b

Counts

112 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
7.5b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
16.5b	(* (/ 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))))
21.0b	(/ (+ (* 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)))

rewrite117.0ms

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))))
30.0ms	(/ (+ (* 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)))

series104.0ms

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))
40.0ms	(* (/ 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))))
52.0ms	(/ (+ (* 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)))

simplify95.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4960	7444
1	4960	7444

prune518.0ms

Filtered

108 candidates to 172 candidates (-59.3%)

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

localize35.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
15.2b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
15.2b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
15.2b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite52.0ms

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:

12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z))
13.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
14.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series66.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5333	1626

prune336.0ms

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

regimes313.0ms

Accuracy

97.8% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.4b

bsearch49.0ms

Steps

Iters	Range		Point
10	1.6144549921576842e+34	2.141706866816348e+52	6.659157927369132e+51
7	-6.808222080754428e+71	-2.956279226014015e+69	-1.811686177481418e+70

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	128	73
1	128	73

end0.0ms

sample823.0ms

Algorithm

intervals

Results

645.0ms	8000×	body	80	valid
1.0ms	8×	body	80	invalid

Details

analyze979.0ms

sample31.0ms

simplify34.0ms

prune11.0ms

localize26.0ms

rewrite59.0ms

series58.0ms

simplify48.0ms

prune242.0ms

localize31.0ms

rewrite60.0ms

series66.0ms

simplify39.0ms

prune323.0ms

localize28.0ms

rewrite117.0ms

series104.0ms

simplify95.0ms

prune518.0ms

localize35.0ms

rewrite52.0ms

series66.0ms

simplify71.0ms

prune336.0ms

regimes313.0ms

bsearch49.0ms

simplify2.0ms

end0.0ms

sample823.0ms

Profiling