Details

sample36.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	18
1	138	18
2	450	18
3	1597	18
4	5001	18

prune5.0ms

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: 29.7b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
28.8b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

14.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
12.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
8.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
35.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series493.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
58.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
76.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
278.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify103.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	657	1279
1	3241	1119
2	5002	1119

prune482.0ms

Filtered

103 candidates to 76 candidates (73.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
19.9b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
20.1b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
23.6b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

13.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
23.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
64.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
29.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
143.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
266.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
365.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify144.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	894	5675
1	3611	5204
2	5002	5070

prune893.0ms

Filtered

217 candidates to 142 candidates (65.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	218	8	226

Merged error: 0.0b

Counts

226 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
19.9b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
25.4b	(/ (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
36×	`times-frac`
30×	`sqrt-prod`
29×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`sqrt-div`
7×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `flip3-+` `flip-+` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`associate-/r/` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`flip3--` `div-sub` `associate-*l/` `flip--`

Counts

4 → 124

Calls

4 calls:

13.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
19.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
57.0ms	(/ (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
85.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
143.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
272.0ms	(/ (* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify102.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	637	2771
1	2611	2494
2	5001	2398

prune603.0ms

Filtered

136 candidates to 91 candidates (66.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	136	8	144

Merged error: 0.0b

Counts

144 → 8

localize44.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.4b	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
19.9b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
26.4b	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

287×	`times-frac`
246×	`add-sqr-sqrt`
182×	`*-un-lft-identity`
132×	`add-cube-cbrt`
112×	`associate-l`
93×	`sqrt-prod`
33×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube`
25×	`distribute-lft-out--` `difference-of-squares`
19×	`cbrt-prod`
16×	`unswap-sqr`
10×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow1` `cbrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `div-inv`
5×	`associate-/l*`
4×	`add-log-exp`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 269

Calls

4 calls:

18.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
20.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
115.0ms	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
164.0ms	(cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
145.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
1.0s	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (fabs (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (cbrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

simplify146.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1546	10457
1	5001	9891

prune1.7s

Filtered

281 candidates to 206 candidates (73.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	280	9	289

Merged error: 0.0b

Counts

289 → 9

regimes420.0ms

Accuracy

94.6% (1.3b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 24.9b

bsearch339.0ms

Steps

Iters	Range		Point
10	0.000608309806168642	2529654550.545884	2485685511.02154
9	-1.0467233090565783e+63	-5.3768555360377445e+54	-2.638876703080918e+59

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	33
1	65	33
2	65	33

end0.0ms

sample756.0ms

Algorithm

intervals

Results

574.0ms

8010×

body

valid