Details

sample38.0ms

Algorithm

intervals

Results

23.0ms

257×

body

valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	37
1	55	37
2	137	37
3	333	37
4	1038	37
5	4169	37
done	5000	37

prune4.0ms

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: 24.7b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
23.8b	(/ (* (- 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:

8.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
11.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
17.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
33.0ms	(/ (* (- 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))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
4.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
10.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
48.0ms	(/ (* (- 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))

simplify729.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	226	2606
1	675	2572
2	2760	2212
done	5001	2212

prune276.0ms

Filtered

77 candidates to 103 candidates (-33.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Merged error: 0.0b

Counts

104 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.3b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
21.5b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
110×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
74×	`add-cube-cbrt`
18×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
10×	`flip3-+` `flip-+`
8×	`pow1` `div-inv` `associate-/l*`
6×	`associate-r` `associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 184

Calls

4 calls:

10.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
14.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
32.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
32.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series106.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
10.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
49.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
43.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify859.0ms

Counts

196 → 196

Iterations

Useful iterations: 2 (311.0ms)

Iter	Nodes	Cost
0	349	10043
1	978	9879
2	3716	9429
done	5000	9429

prune702.0ms

Filtered

147 candidates to 196 candidates (-33.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	196	7	203

Merged error: 0b

Counts

203 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (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))) (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))))
21.5b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
21.5b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
21.5b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
72×	`cbrt-prod`
69×	`times-frac`
60×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr` `associate-r` `associate-l`
14×	`associate-/r/`
12×	`add-exp-log`
11×	`pow1`
10×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`associate-/r` `associate-/l` `unswap-sqr`
7×	`div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 177

Calls

4 calls:

65.0ms	(* (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))) (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))))
32.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
31.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
31.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series202.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (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))) (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))))
38.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
42.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
38.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify470.0ms

Counts

189 → 189

Iterations

Useful iterations: done (456.0ms)

Iter	Nodes	Cost
0	228	12437
1	454	12069
2	1494	11383
done	5002	11294

prune1.5s

Filtered

148 candidates to 189 candidates (-27.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	189	7	196

Merged error: 0b

Counts

196 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

19.6b	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
19.6b	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
19.6b	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
23.8b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

9.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
9.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
9.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
41.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

series100.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
13.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
12.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
63.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (* (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x)) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) (cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))) 313.399215894) x) 47.066876606))

simplify573.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (170.0ms)

Iter	Nodes	Cost
0	196	3603
1	549	3551
2	2109	2346
done	5000	2346

prune324.0ms

Filtered

69 candidates to 76 candidates (-10.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	76	7	83

Merged error: 0b

Counts

83 → 7

regimes316.0ms

Accuracy

97.5% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.9b

bsearch56.0ms

Steps

Iters	Range		Point
8	1.3591990794494764e+66	4.1266864370833114e+68	2.8089106367080938e+66
9	-2.5455472253050984e+57	-8.761369592446147e+49	-2.6115178047519778e+50

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	67
1	60	57
done	60	57

end0.0ms

sample1.1s

Algorithm

intervals

Results

744.0ms

8018×

body

valid

Details

sample38.0ms

simplify1.3s

prune4.0ms

localize25.0ms

rewrite72.0ms

series68.0ms

simplify729.0ms

prune276.0ms

localize25.0ms

rewrite99.0ms

series106.0ms

simplify859.0ms

prune702.0ms

localize35.0ms

rewrite167.0ms

series202.0ms

simplify470.0ms

prune1.5s

localize34.0ms

rewrite70.0ms

series100.0ms

simplify573.0ms

prune324.0ms

regimes316.0ms

bsearch56.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling