Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify162.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	9	19
1	19	18
2	39	18
3	80	18
4	133	18
5	187	18
6	215	18
7	219	18
done	219	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
2.8b	(- (* x x) (* (* y 4.0) y))
31.7b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma x x (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(fma x x (* (* y 4.0) y))
57.0ms	(- (* x x) (* (* y 4.0) y))
85.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify1.7s

Counts

67 → 67

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	94	1321
1	224	1289
2	802	1165
3	3685	1163
done	5000	1161

prune214.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune10.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
2.3b	(fma x x (- (* (* y 4.0) y)))
31.7b	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma x x (* (* y 4.0) y))
0.0ms	(fma x x (- (* (* y 4.0) y)))
2.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma x x (* (* y 4.0) y))
58.0ms	(fma x x (- (* (* y 4.0) y)))
84.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

simplify711.0ms

Counts

58 → 58

Iterations

Useful iterations: done (709.0ms)

Iter	Nodes	Cost
0	71	1123
1	121	1114
2	291	1005
3	1030	1005
done	5000	1004

prune172.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y))))
0.0b	(log (exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))))
2.3b	(fma x x (- (* (* y 4.0) y)))
31.7b	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
26×	`exp-prod`
14×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-/r` `div-inv` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `fma-udef` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

4.0ms	(exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y))))
5.0ms	(log (exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))))
0.0ms	(fma x x (- (* (* y 4.0) y)))
3.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y))))
78.0ms	(log (exp (/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))))
55.0ms	(fma x x (- (* (* y 4.0) y)))
80.0ms	(/ (fma x x (- (* (* y 4.0) y))) (fma x x (* (* y 4.0) y)))

simplify653.0ms

Counts

101 → 101

Iterations

Useful iterations: done (650.0ms)

Iter	Nodes	Cost
0	116	2190
1	172	2109
2	353	1927
3	1123	1927
done	5002	1926

prune325.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes118.0ms

Accuracy

57.9% (13.2b remaining)

Error of 13.6b against oracle of 0.4b and baseline of 31.7b

bsearch233.0ms

Steps

Iters	Range		Point
9	4.283497980630725e+128	1.2086931281044804e+136	4.367447801126625e+128
8	4.2706539415928307e+104	2.1878188410446244e+107	2.1620145518824135e+107
9	1.855235282084144e+33	6.217793645765005e+41	4.011625031578035e+38
6	2231369.5462890854	28638621.607503247	28161126.972837694
8	6.0695211452904165e-58	2.2556006266800907e-55	1.1196094733529732e-55
7	-2.4883474419946845e-96	-1.2073393430268885e-97	-1.3841596065667632e-97
6	-3.1442305190809916e+143	-5.062787100137526e+142	-7.710738992849757e+142

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	93
1	42	93
2	49	93
done	49	93

end0.0ms

sample377.0ms

Algorithm

intervals

Results

241.0ms

8000×

body

valid