Details

sample50.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify935.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2054
4	2054
3	709
2	152
1	33
0	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* i i) 1/4)
0.0b	(* (* i i) 4)
12.6b	(/ (* (* i i) 1/4) (- (* (* i i) 4) 1.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cbrt-cube` `add-exp-log`
13×	`pow1`
9×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `pow-prod-down`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--` `associate-/l*`

Counts

3 → 72

Calls

3 calls:

15.0ms	(* (* i i) 1/4)
19.0ms	(* (* i i) 4)
78.0ms	(/ (* (* i i) 1/4) (- (* (* i i) 4) 1.0))

series187.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (* i i) 1/4)
48.0ms	(* (* i i) 4)
103.0ms	(/ (* (* i i) 1/4) (- (* (* i i) 4) 1.0))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	2012
3	2012
2	1337
1	351
0	134

prune647.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* i i) 4)
12.6b	(/ (* i (* i 1/4)) (- (* (* i i) 4) 1.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-r*` `pow-prod-down`
2×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`clear-num` `frac-2neg` `flip3--` `associate-l` `-commutative` `div-inv` `flip--` `associate-/l` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

21.0ms	(* (* i i) 4)
60.0ms	(/ (* i (* i 1/4)) (- (* (* i i) 4) 1.0))

series146.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(* (* i i) 4)
117.0ms	(/ (* i (* i 1/4)) (- (* (* i i) 4) 1.0))

simplify1.3s

Counts

56 → 56

Iterations

Iter	Nodes
done	2115
3	2115
2	1539
1	372
0	125

prune434.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

10.8b	(cbrt (* (* (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))))
12.3b	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
12.3b	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
12.3b	(* (- (* 4 (* i i)) 1.0) (/ 4 i))

rewrite892.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
39×	`associate-r`
30×	`times-frac`
28×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
11×	`frac-times` `associate-*l/`
10×	`pow1`
9×	`associate-l`
7×	`cbrt-div`
6×	`flip3--` `prod-exp` `associate-*r/` `cbrt-unprod` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 137

Calls

4 calls:

644.0ms	(cbrt (* (* (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))))
74.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
83.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
89.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))

series663.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (* (* (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))) (/ i (* (- (* 4 (* i i)) 1.0) (/ 4 i)))))
200.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
167.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))
196.0ms	(* (- (* 4 (* i i)) 1.0) (/ 4 i))

simplify1.2s

Counts

149 → 149

Iterations

Iter	Nodes
done	2049
3	2049
2	1341
1	358
0	150

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.015625 (/ 1 (* i i)) (fma (/ (/ 1 (* i i)) (* i i)) 0.00390625 1/16))
0.1b	(/ (/ 1 (* i i)) (* i i))
0.7b	(/ 1 (* i i))
0.7b	(/ 1 (* i i))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

75×	`pow1`
71×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`pow-flip`
30×	`div-exp`
22×	`pow-div`
19×	`times-frac` `prod-exp`
14×	`cbrt-undiv`
13×	`associate-/l*`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
8×	`rec-exp` `1-exp`
7×	`pow-prod-down` `cbrt-unprod`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `inv-pow` `add-log-exp`
3×	`clear-num` `associate-/r*` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

4 → 152

Calls

4 calls:

0.0ms	(fma 0.015625 (/ 1 (* i i)) (fma (/ (/ 1 (* i i)) (* i i)) 0.00390625 1/16))
23.0ms	(/ (/ 1 (* i i)) (* i i))
17.0ms	(/ 1 (* i i))
13.0ms	(/ 1 (* i i))

series146.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma 0.015625 (/ 1 (* i i)) (fma (/ (/ 1 (* i i)) (* i i)) 0.00390625 1/16))
49.0ms	(/ (/ 1 (* i i)) (* i i))
29.0ms	(/ 1 (* i i))
19.0ms	(/ 1 (* i i))

simplify1.0s

Counts

164 → 164

Iterations

Iter	Nodes
done	2010
3	2010
2	898
1	310
0	134

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch84.0ms

Steps

Iters	Range		Point
9	576.6029367193106	2362941202.8442736	1645.4224050168862

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
271.0ms	8000×	pre	80	true