Details

sample20.0ms

Algorithm

intervals

Results

4.0ms	196×	body	80	valid
4.0ms	15×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	10×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4
done	5002	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.7b	(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×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

11.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series92.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ y (+ y 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify108.0ms

Counts

51 → 51

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228
done	5002	228

prune130.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

4.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
35.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
3.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series345.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ y 1.0))
91.0ms	(cbrt (+ y 1.0))
105.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
58.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify50.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	370	879
1	1298	813
2	5001	756
done	5001	756

prune334.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ y 1.0)))
0.3b	(cbrt (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
10.7b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

386×	`cbrt-div`
136×	`frac-times`
110×	`flip3-+` `flip-+`
50×	`associate-*r/`
44×	`associate-*l/`
26×	`cbrt-prod`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-exp-log`
12×	`pow1/3`
11×	`add-cube-cbrt`
10×	`add-sqr-sqrt`
9×	`pow-prod-down`
7×	`associate-l`
6×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
1×	`swap-sqr` `associate-r` `pow-sqr` `*-commutative` `fma-udef`

Counts

4 → 159

Calls

4 calls:

4.0ms	(cbrt (cbrt (+ y 1.0)))
4.0ms	(cbrt (cbrt (+ y 1.0)))
216.0ms	(* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series579.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (cbrt (+ y 1.0)))
95.0ms	(cbrt (cbrt (+ y 1.0)))
328.0ms	(* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
62.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify90.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	864	3580
1	2257	3438
2	5002	3224
done	5002	3224

prune603.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
6.8b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0))))) (- x 1.0) 1.0)
15.4b	(cbrt (- (* y y) (* 1.0 1.0)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

104×	`cbrt-prod`
77×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
56×	`times-frac`
47×	`add-cube-cbrt`
18×	`cbrt-div` `difference-of-squares`
11×	`pow1`
9×	`swap-sqr`
8×	`add-exp-log` `associate-/r*` `distribute-lft-out--`
7×	`pow1/3` `associate-r` `associate-l` `associate-/l*`
6×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 170

Calls

4 calls:

26.0ms	(/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0)))
35.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0))))) (- x 1.0) 1.0)
6.0ms	(cbrt (- (* y y) (* 1.0 1.0)))

series646.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0)))
112.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
190.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (/ (cbrt (- (* y y) (* 1.0 1.0))) (cbrt (- y 1.0))))) (- x 1.0) 1.0)
206.0ms	(cbrt (- (* y y) (* 1.0 1.0)))

simplify95.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	697	2098
1	2664	2006
2	5001	1926
done	5001	1926

prune650.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

regimes100.0ms

Accuracy

97.9% (0.1b remaining)

Error of 7.6b against oracle of 7.4b and baseline of 14.3b

bsearch85.0ms

Steps

Iters	Range		Point
8	1.6262670109576334e+32	4.037166448428983e+35	1.6618012416610568e+32
10	-5.3372167004463374e+19	-417378.0376052807	-1.210662606949831e+16

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9
done	23	9

end0.0ms

sample469.0ms

Algorithm

intervals

Results

142.0ms	6109×	body	80	valid
67.0ms	698×	body	640	valid
45.0ms	402×	body	1280	valid
32.0ms	522×	body	320	valid
11.0ms	269×	body	160	valid