Details

sample36.0ms

Algorithm

intervals

Results

22.0ms

257×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	37
1	55	37
2	137	37
3	330	37
4	1017	37
5	3989	37
done	5001	37

prune3.0ms

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

localize31.0ms

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))

rewrite68.0ms

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)
14.0ms	(* (+ (* (+ (* (+ (* 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:

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)
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))

simplify1.2s

Counts

103 → 103

Iterations

Useful iterations: 2 (434.0ms)

Iter	Nodes	Cost
0	226	2606
1	666	2572
2	2694	2224
done	5001	2224

prune259.0ms

Filtered

78 candidates to 103 candidates (-32.1%)

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)
30.0ms	(/ (- 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))

series92.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ x 43.3400022514) x) 263.505074721) x)
9.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
44.0ms	(/ (- 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))

simplify1.4s

Counts

196 → 196

Iterations

Useful iterations: 2 (734.0ms)

Iter	Nodes	Cost
0	349	10043
1	974	9879
2	3393	9441
done	5000	9441

prune668.0ms

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))

rewrite160.0ms

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:

62.0ms	(* (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))))
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))
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))
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))

series187.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (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))))
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))
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))

simplify2.6s

Counts

189 → 189

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	228	12437
1	452	12061
2	1355	11383
3	4585	10516
done	5000	10516

prune1.8s

Filtered

149 candidates to 189 candidates (-26.8%)

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

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.2b	(* 43.3400022514 (pow x 2))
8.3b	(+ (* 43.3400022514 (pow x 2)) (pow x 3))
23.8b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (pow x 2)) (pow x 3))) 313.399215894) x) 47.066876606))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
8×	`associate-/l/`
6×	`pow1` `flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp` `unswap-sqr`
4×	`frac-times` `unpow-prod-down` `associate-*l/`
3×	`flip3--` `times-frac` `associate-/r*` `flip--` `cbrt-unprod`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r/` `-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

14.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
6.0ms	(* 43.3400022514 (pow x 2))
10.0ms	(+ (* 43.3400022514 (pow x 2)) (pow x 3))
33.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (pow x 2)) (pow x 3))) 313.399215894) x) 47.066876606))

series64.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
3.0ms	(* 43.3400022514 (pow x 2))
8.0ms	(+ (* 43.3400022514 (pow x 2)) (pow x 3))
44.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (pow x 2)) (pow x 3))) 313.399215894) x) 47.066876606))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: 2 (502.0ms)

Iter	Nodes	Cost
0	222	2676
1	628	2606
2	2427	2253
done	5001	2253

prune239.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	101	7	108

Merged error: 0b

Counts

108 → 7

regimes291.0ms

Accuracy

97.5% (0.6b remaining)

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

bsearch53.0ms

Steps

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

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample1.0s

Algorithm

intervals

Results

705.0ms

8018×

body

valid

Details

sample36.0ms

simplify2.0s

prune3.0ms

localize31.0ms

rewrite68.0ms

series68.0ms

simplify1.2s

prune259.0ms

localize27.0ms

rewrite95.0ms

series92.0ms

simplify1.4s

prune668.0ms

localize34.0ms

rewrite160.0ms

series187.0ms

simplify2.6s

prune1.8s

localize27.0ms

rewrite65.0ms

series64.0ms

simplify1.2s

prune239.0ms

regimes291.0ms

bsearch53.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling