Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify223.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	252
7	252
6	244
5	199
4	133
3	77
2	39
1	19
0	9

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize29.0ms

Local error

Found 2 expressions with local error:

1.5b	(fma (* y 4.0) (- y) (* x x))
29.1b	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (* y 4.0) (- y) (* x x))
7.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

series229.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(fma (* y 4.0) (- y) (* x x))
132.0ms	(/ (fma (* y 4.0) (- y) (* x x)) (fma y (* y 4.0) (* x x)))

simplify1.4s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	2061
2	344
1	118
0	67

prune366.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3))
0.0b	(pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3)
3.3b	(fma 4.0 (* y (- y)) (* x x))
29.1b	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cube-div` `cube-mult` `cbrt-undiv` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `clear-num` `pow-pow` `frac-2neg` `pow1/3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 131

Calls

4 calls:

5.0ms	(cbrt (pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3))
5.0ms	(pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3)
0.0ms	(fma 4.0 (* y (- y)) (* x x))
5.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3))
142.0ms	(pow (/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y)))) 3)
80.0ms	(fma 4.0 (* y (- y)) (* x x))
107.0ms	(/ (fma 4.0 (* y (- y)) (* x x)) (fma x x (* y (* 4.0 y))))

simplify1.8s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2520
1	451
0	150

prune705.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x))))
3.3b	(fma 4.0 (* y (- y)) (* x x))
29.1b	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`associate-/r/` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 117

Calls

3 calls:

14.0ms	(/ 1 (/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x))))
0.0ms	(fma 4.0 (* y (- y)) (* x x))
5.0ms	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))

series337.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(/ 1 (/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x))))
101.0ms	(fma 4.0 (* y (- y)) (* x x))
122.0ms	(/ (fma x x (* y (* 4.0 y))) (fma 4.0 (* y (- y)) (* x x)))

simplify1.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1844
1	378
0	168

prune618.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.6b

regimes154.0ms

Accuracy

56.8% (13.4b remaining)

Error of 13.8b against oracle of 0.3b and baseline of 31.5b

bsearch252.0ms

Steps

Iters	Range		Point
9	1.8841348729660574e+121	3.270754152227266e+128	7.3735183150701e+127
6	1.9438090553147822e-153	1.5544812808461908e-152	2.1395518106041052e-153
7	-2.6703146002526768e+20	-6.809545746203195e+18	-9.211266202426182e+18
7	-4.6693392046439585e+80	-2.8553313065515472e+79	-4.332313917220749e+80
8	-1.4870231680618705e+126	-3.431305599926169e+122	-4.754864512281886e+122

simplify10.0ms

Iterations

Iter	Nodes
done	38
1	38
0	31

end0.0ms

sample765.0ms

Algorithm

intervals

Results

558.0ms

8000×

body

valid