Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	204×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	9×	body	1280	valid
1.0ms	10×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	161	10
5	466	10
6	1868	10
done	5000	10

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
11.8b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

32.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- x 1.0) (+ y 1.0))
100.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	114	834
1	282	799
2	1133	747
done	5002	743

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
0.1b	(* (/ (- x 1.0) (+ y 1.0)) y)
4.4b	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-l`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3--` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip--`

Counts

3 → 109

Calls

3 calls:

24.0ms	(/ (- x 1.0) (+ y 1.0))
53.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
19.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

series252.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (- x 1.0) (+ y 1.0))
98.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
112.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

simplify3.1s

Counts

118 → 118

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	172	1520
1	472	1433
2	2182	1346
done	5002	1338

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.1b	(* (- x 1.0) (/ 1 (+ y 1.0)))
0.1b	(* (* (- x 1.0) (/ 1 (+ y 1.0))) y)
4.4b	(+ (* (* (- x 1.0) (/ 1 (+ y 1.0))) y) 1.0)

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
32×	`add-exp-log` `add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
10×	`associate-*l/`
7×	`cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `pow-prod-down` `associate-/r*` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l*` `unswap-sqr`
2×	`associate-r/` `un-div-inv` `-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

24.0ms	(/ 1 (+ y 1.0))
87.0ms	(* (- x 1.0) (/ 1 (+ y 1.0)))
78.0ms	(* (* (- x 1.0) (/ 1 (+ y 1.0))) y)
144.0ms	(+ (* (* (- x 1.0) (/ 1 (+ y 1.0))) y) 1.0)

series310.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (+ y 1.0))
73.0ms	(* (- x 1.0) (/ 1 (+ y 1.0)))
73.0ms	(* (* (- x 1.0) (/ 1 (+ y 1.0))) y)
135.0ms	(+ (* (* (- x 1.0) (/ 1 (+ y 1.0))) y) 1.0)

simplify4.7s

Counts

144 → 144

Iterations

Useful iterations: done (4.7s)

Iter	Nodes	Cost
0	205	1857
1	569	1638
2	4361	1328
done	5000	1326

prune330.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (- x 1.0) (/ y (+ y 1.0)) 1.0))
2.4b	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
2.4b	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
2.4b	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (- x 1.0) (/ y (+ y 1.0)) 1.0))
0.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
0.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
0.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)

series621.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(cbrt (fma (- x 1.0) (/ y (+ y 1.0)) 1.0))
75.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
83.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)
83.0ms	(fma (- x 1.0) (/ y (+ y 1.0)) 1.0)

simplify2.2s

Counts

55 → 55

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	76	843
1	179	832
2	560	731
3	2532	692
done	5001	686

prune305.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes76.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.8b

bsearch86.0ms

Steps

Iters	Range		Point
8	13587.758917488305	805653349.9608173	216523043.9852226
8	-20631429316545348.0	-1950712569354.648	-1979426812970.8699

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	19	39
1	27	30
done	27	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

603.0ms	772×	body	640	valid
329.0ms	6055×	body	80	valid
80.0ms	511×	body	320	valid
74.0ms	361×	body	1280	valid
24.0ms	301×	body	160	valid