Details

sample36.0ms

Algorithm

intervals

Results

22.0ms

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

localize24.0ms

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))

rewrite70.0ms

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)
10.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
17.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
32.0ms	(/ (* (- 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))

series64.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (+ (* 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)
44.0ms	(/ (* (- 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))

simplify767.0ms

Counts

103 → 103

Iterations

Useful iterations: done (760.0ms)

Iter	Nodes	Cost
0	226	2606
1	675	2577
2	2973	2227
done	5001	2216

prune266.0ms

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

localize27.0ms

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))

rewrite95.0ms

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)
29.0ms	(/ (- 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)))
28.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series97.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
45.0ms	(/ (- 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)))
35.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify857.0ms

Counts

196 → 196

Iterations

Useful iterations: done (845.0ms)

Iter	Nodes	Cost
0	349	10043
1	978	9888
2	3790	9443
done	5000	9431

prune678.0ms

Filtered

146 candidates to 196 candidates (-34.2%)

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

localize34.0ms

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))

rewrite164.0ms

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

series189.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (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))))
36.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
40.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))
35.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify495.0ms

Counts

189 → 189

Iterations

Useful iterations: done (480.0ms)

Iter	Nodes	Cost
0	228	12437
1	454	12102
2	1548	11389
done	5000	10715

prune1.6s

Filtered

153 candidates to 189 candidates (-23.5%)

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

localize33.0ms

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))

rewrite68.0ms

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:

8.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
8.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
8.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
40.0ms	(/ (* (- 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))

series93.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
11.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
11.0ms	(cbrt (* (+ (* (+ x 43.3400022514) x) 263.505074721) x))
59.0ms	(/ (* (- 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))

simplify583.0ms

Counts

76 → 76

Iterations

Useful iterations: done (579.0ms)

Iter	Nodes	Cost
0	196	3603
1	549	3553
2	2165	2352
done	5000	2346

prune311.0ms

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

regimes299.0ms

Accuracy

97.5% (0.6b remaining)

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

bsearch57.0ms

Steps

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

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	42	67
1	60	57
2	61	57
done	61	57

end0.0ms

sample1.0s

Algorithm

intervals

Results

705.0ms

8018×

body

valid

Details

sample36.0ms

simplify1.3s

prune4.0ms

localize24.0ms

rewrite70.0ms

series64.0ms

simplify767.0ms

prune266.0ms

localize27.0ms

rewrite95.0ms

series97.0ms

simplify857.0ms

prune678.0ms

localize34.0ms

rewrite164.0ms

series189.0ms

simplify495.0ms

prune1.6s

localize33.0ms

rewrite68.0ms

series93.0ms

simplify583.0ms

prune311.0ms

regimes299.0ms

bsearch57.0ms

simplify6.0ms

end0.0ms

sample1.0s

Profiling