Details

sample37.0ms

Algorithm

intervals

Results

8.0ms	193×	body	80	valid
5.0ms	12×	body	160	valid
4.0ms	20×	body	640	valid
2.0ms	20×	body	320	valid
2.0ms	11×	body	1280	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite20.0ms

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:

18.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series157.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ y (+ y 1.0))
76.0ms	(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

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize48.0ms

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))
11.9b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series478.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (+ y 1.0))
139.0ms	(cbrt (+ y 1.0))
128.0ms	(cbrt (+ y 1.0))
81.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	3523
2	773
1	240
0	105

prune664.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(cbrt (cbrt (+ y 1.0)))
10.9b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
16×	`cbrt-prod`
11×	`*-un-lft-identity`
8×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-l/` `associate-r/` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 64

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
14.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
15.0ms	(cbrt (cbrt (+ y 1.0)))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

series575.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (+ y 1.0))
172.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
137.0ms	(cbrt (cbrt (+ y 1.0)))
101.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1444
1	475
0	222

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
12.1b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- 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)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt y)
364.0ms	(cbrt y)
299.0ms	(cbrt y)
168.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	1485
2	337
1	110
0	55

prune355.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.7b

regimes397.0ms

Accuracy

96.4% (0.3b remaining)

Error of 7.4b against oracle of 7.1b and baseline of 14.8b

bsearch182.0ms

Steps

Iters	Range		Point
6	1.7322668861585903e+49	8.629181688698077e+49	3.069168683971201e+49
10	-6.926400201851654e+19	-409088.2864877689	-2404433391549375.0

simplify17.0ms

Iterations

Iter	Nodes
done	40
1	40
0	31

end0.0ms

sample1.5s

Algorithm

intervals

Results

836.0ms	6102×	body	80	valid
231.0ms	744×	body	640	valid
116.0ms	538×	body	320	valid
80.0ms	336×	body	1280	valid
25.0ms	280×	body	160	valid