Details

sample35.0ms

Algorithm

intervals

Results

19.0ms

274×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.3b	(fma a c (* b d))
24.6b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite14.0ms

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:

1.0ms	(fma c c (* d d))
1.0ms	(fma a c (* b d))
11.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma c c (* d d))
80.0ms	(fma a c (* b d))
163.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify945.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	73	833
1	115	819
2	321	707
3	1215	707
done	5000	707

prune280.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.3b	(fma a c (* d b))
15.2b	(/ (fma a c (* d b)) (hypot d c))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

50.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.0ms	(fma a c (* d b))
5.0ms	(/ (fma a c (* d b)) (hypot d c))

series538.0ms

Counts

3 → 9

Calls

3 calls:

258.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
65.0ms	(fma a c (* d b))
215.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify2.3s

Counts

106 → 106

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	138	1895
1	382	1844
2	2406	1544
done	5000	1527

prune449.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.3b	(fma a c (* d b))
15.2b	(/ (fma a c (* d b)) (hypot d c))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

11.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.0ms	(fma a c (* d b))
5.0ms	(/ (fma a c (* d b)) (hypot d c))

series480.0ms

Counts

3 → 9

Calls

3 calls:

215.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
54.0ms	(fma a c (* d b))
210.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify937.0ms

Counts

120 → 120

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	159	2484
1	362	2426
2	1752	2255
done	5000	2212

prune451.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
0.3b	(fma a c (* d b))
15.4b	(* (fma a c (* d b)) (/ 1 (hypot d c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `associate-/l`

Counts

3 → 77

Calls

3 calls:

18.0ms	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
0.0ms	(fma a c (* d b))
26.0ms	(* (fma a c (* d b)) (/ 1 (hypot d c)))

series376.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
48.0ms	(fma a c (* d b))
174.0ms	(* (fma a c (* d b)) (/ 1 (hypot d c)))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: 2 (216.0ms)

Iter	Nodes	Cost
0	118	1355
1	301	1288
2	2054	986
done	5000	986

prune259.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

regimes251.0ms

Accuracy

32.2% (7.7b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 16.9b

bsearch78.0ms

Steps

Iters	Range		Point
8	3.909580657839742e+222	1.7405675075945448e+227	5.396385525097289e+222
6	-8.945616726736062e+128	-9.921620365554097e+127	-1.9122070425426486e+128

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	24	35
2	26	35
done	26	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

670.0ms

8393×

body

valid