Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5148
4	3823
3	744
2	157
1	32
0	10

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* (* 2.0 2.0) i) (/ 1.0 i))
0.3b	(/ (/ i (* 2.0 2.0)) (- (* (* 2.0 2.0) i) (/ 1.0 i)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`prod-diff`
11×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

2 → 80

Calls

2 calls:

38.0ms	(- (* (* 2.0 2.0) i) (/ 1.0 i))
54.0ms	(/ (/ i (* 2.0 2.0)) (- (* (* 2.0 2.0) i) (/ 1.0 i)))

series220.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(- (* (* 2.0 2.0) i) (/ 1.0 i))
142.0ms	(/ (/ i (* 2.0 2.0)) (- (* (* 2.0 2.0) i) (/ 1.0 i)))

simplify2.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	2221
1	661
0	243

prune537.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* i i) (* i i))
0.1b	(* (* i i) i)
0.1b	(* (* i i) i)
0.1b	(* (* (* i i) i) (* (* i i) i))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

695×	`pow1`
326×	`pow-prod-up`
221×	`pow-plus`
120×	`pow-prod-down`
112×	`pow-sqr`
70×	`pow2`
62×	`add-cbrt-cube` `add-exp-log`
41×	`prod-exp` `cbrt-unprod`
24×	`pow3`
8×	`add-sqr-sqrt` `associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`swap-sqr`

Counts

4 → 318

Calls

4 calls:

40.0ms	(* (* i i) (* i i))
17.0ms	(* (* i i) i)
17.0ms	(* (* i i) i)
171.0ms	(* (* (* i i) i) (* (* i i) i))

series221.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* i i) (* i i))
46.0ms	(* (* i i) i)
42.0ms	(* (* i i) i)
84.0ms	(* (* (* i i) i) (* (* i i) i))

simplify4.6s

Counts

330 → 330

Iterations

Iter	Nodes
done	5001
3	3411
2	724
1	319
0	113

prune486.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 0.00390625 (* i i)) (* i i)) (+ (/ 0.015625 (* i i)) 0.0625))
0.1b	(/ (/ 0.00390625 (* i i)) (* i i))
0.2b	(/ 0.00390625 (* i i))
0.2b	(/ 0.015625 (* i i))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-cbrt-cube` `add-exp-log`
29×	`times-frac`
20×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`cbrt-undiv` `div-exp`
13×	`associate-/l*`
11×	`fma-def`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `associate-/r*` `sum-log` `frac-2neg` `distribute-lft-out`
2×	`flip3-+` `frac-add` `flip-+`
1×	`+-commutative` `associate-+r+` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

103.0ms	(+ (/ (/ 0.00390625 (* i i)) (* i i)) (+ (/ 0.015625 (* i i)) 0.0625))
15.0ms	(/ (/ 0.00390625 (* i i)) (* i i))
15.0ms	(/ 0.00390625 (* i i))
8.0ms	(/ 0.015625 (* i i))

series210.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (/ (/ 0.00390625 (* i i)) (* i i)) (+ (/ 0.015625 (* i i)) 0.0625))
51.0ms	(/ (/ 0.00390625 (* i i)) (* i i))
51.0ms	(/ 0.00390625 (* i i))
49.0ms	(/ 0.015625 (* i i))

simplify1.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2191
1	485
0	169

prune468.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* i i) (* i i))
13.9b	(/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0))
41.2b	(/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i)))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

302×	`add-cbrt-cube` `add-exp-log`
168×	`prod-exp` `cbrt-unprod`
114×	`pow1`
76×	`cbrt-undiv` `div-exp`
36×	`pow-prod-up`
26×	`times-frac`
23×	`pow-prod-down`
22×	`pow-sqr`
20×	`add-sqr-sqrt`
18×	`pow-plus`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow2`
7×	`div-inv`
6×	`associate-/l*` `difference-of-squares`
5×	`associate-/r*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3--` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--` `unswap-sqr` `associate-/l/`

Counts

3 → 226

Calls

3 calls:

30.0ms	(* (* i i) (* i i))
125.0ms	(/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0))
84.0ms	(/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (* i i) (* i i))
105.0ms	(/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0))
51.0ms	(/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i)))

simplify2.9s

Counts

235 → 235

Iterations

Iter	Nodes
done	5042
2	4175
1	873
0	283

prune448.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes90.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch42.0ms

Steps

Iters	Range		Point
7	0.06240887830975301	4.4742802149053365	0.4965227290920667

simplify4.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

906.0ms	8000×	body	80	valid
100.0ms	8000×	pre	80	true