Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	201×	body	80	valid
3.0ms	17×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	6×	body	1280	valid
1.0ms	11×	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
4.3b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite11.0ms

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:

9.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series151.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ y (+ y 1.0))
90.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify1.0s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	898
1	213
0	94

prune363.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ y 1.0))
0.2b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.6b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite77.0ms

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×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

7.0ms	(cbrt (+ y 1.0))
6.0ms	(cbrt (+ y 1.0))
51.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series484.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (+ y 1.0))
128.0ms	(cbrt (+ y 1.0))
158.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
78.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1512
1	398
0	170

prune809.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.5b

localize70.0ms

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 (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
11.8b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

4.0ms	(cbrt (cbrt (+ y 1.0)))
9.0ms	(cbrt (cbrt (+ y 1.0)))
56.0ms	(* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series468.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (cbrt (+ y 1.0)))
128.0ms	(cbrt (cbrt (+ y 1.0)))
153.0ms	(* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
71.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	1642
1	431
0	200

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.6b	(* (cbrt y) (cbrt y))
10.9b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
9.0ms	(* (cbrt y) (cbrt y))
0.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

315.0ms	(cbrt y)
276.0ms	(cbrt y)
365.0ms	(* (cbrt y) (cbrt y))
110.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify1.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	942
1	200
0	92

prune472.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

regimes210.0ms

Accuracy

96.4% (0.3b remaining)

Error of 7.7b against oracle of 7.4b and baseline of 14.4b

bsearch149.0ms

Steps

Iters	Range		Point
8	7.855369798947988e+37	6.993988048520301e+40	2.3756135457378515e+39
6	-2.7772760329833916e+20	-3.1196064285525156e+19	-4.297273805816281e+19

simplify15.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

412.0ms	6095×	body	80	valid
180.0ms	381×	body	1280	valid
131.0ms	717×	body	640	valid
121.0ms	535×	body	320	valid
26.0ms	272×	body	160	valid