Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
3.0ms	27×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	12×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1852
5	465
4	160
3	76
2	35
1	16
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.0b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `distribute-lft-out`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

11.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series128.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ y (+ y 1.0))
70.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify707.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	898
1	213
0	94

prune285.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
6.9b	(fma (* (* (/ (cbrt y) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt y)) (/ (cbrt y) (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series929.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt y)
264.0ms	(cbrt y)
275.0ms	(cbrt y)
125.0ms	(fma (* (* (/ (cbrt y) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt y)) (/ (cbrt y) (cbrt (+ 1.0 y)))) (- x 1.0) 1.0)

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	2113
2	391
1	119
0	59

prune446.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
3.0b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
3.0b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
3.0b	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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 (+ 1.0 y)) 1.0))
0.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
0.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
0.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

series582.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
84.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
92.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
83.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

simplify3.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	2474
2	565
1	177
0	76

prune615.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
10.0b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 y) (cbrt y))) (- x 1.0) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt y)
2.0ms	(cbrt y)
2.0ms	(cbrt y)
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 y) (cbrt y))) (- x 1.0) 1.0)

series849.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt y)
217.0ms	(cbrt y)
266.0ms	(cbrt y)
95.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ 1.0 y) (cbrt y))) (- x 1.0) 1.0)

simplify655.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	1399
2	328
1	109
0	55

prune361.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.1b

regimes263.0ms

Accuracy

95.1% (0.4b remaining)

Error of 7.7b against oracle of 7.3b and baseline of 15.1b

bsearch170.0ms

Steps

Iters	Range		Point
10	257785.57693934403	2.1403836343929554e+18	13562637422873356.0
10	-4.352294551030907e+91	-3.979409539042198e+78	-4.057680286744787e+78

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample1000.0ms

Algorithm

intervals

Results

357.0ms	6044×	body	80	valid
157.0ms	774×	body	640	valid
131.0ms	306×	body	1280	valid
70.0ms	569×	body	320	valid
26.0ms	307×	body	160	valid