Details

sample52.0ms

Algorithm

intervals

Results

19.0ms

264×

body

valid

simplify213.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize94.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.2b	(- (* b c) (* a d))
28.8b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma d d (* c c))
37.0ms	(- (* b c) (* a d))
75.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series361.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma d d (* c c))
94.0ms	(- (* b c) (* a d))
193.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify5.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5049
3	3094
2	852
1	233
0	98

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 28.6b

localize123.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
18.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
28.5b	(sqrt (fma d d (* c c)))
28.5b	(sqrt (fma d d (* c c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

32.0ms	(- (* b c) (* a d))
95.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
8.0ms	(sqrt (fma d d (* c c)))
9.0ms	(sqrt (fma d d (* c c)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (* b c) (* a d))
316.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
75.0ms	(sqrt (fma d d (* c c)))
79.0ms	(sqrt (fma d d (* c c)))

simplify4.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2136
2	773
1	266
0	115

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.9b

localize83.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.3b	(fma b c (- (* a d)))
28.8b	(/ (fma b c (- (* a d))) (fma d d (* c c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

2.0ms	(fma d d (* c c))
2.0ms	(fma b c (- (* a d)))
22.0ms	(/ (fma b c (- (* a d))) (fma d d (* c c)))

series403.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma d d (* c c))
87.0ms	(fma b c (- (* a d)))
261.0ms	(/ (fma b c (- (* a d))) (fma d d (* c c)))

simplify3.4s

Counts

61 → 61

Iterations

Iter	Nodes
done	5003
3	1333
2	361
1	128
0	76

prune989.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.9b

localize127.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma d d (* c c))
0.2b	(- (* b c) (* d a))
0.3b	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* d a))))
28.7b	(/ (fma d d (* c c)) (- (* b c) (* d a)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 147

Calls

4 calls:

1.0ms	(fma d d (* c c))
21.0ms	(- (* b c) (* d a))
65.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* d a))))
47.0ms	(/ (fma d d (* c c)) (- (* b c) (* d a)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma d d (* c c))
74.0ms	(- (* b c) (* d a))
295.0ms	(/ 1 (/ (fma d d (* c c)) (- (* b c) (* d a))))
161.0ms	(/ (fma d d (* c c)) (- (* b c) (* d a)))

simplify6.8s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	4536
2	1277
1	488
0	208

prune1.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 15.7b

regimes1.1s

Accuracy

-10.9% (3.5b remaining)

Error of 17.6b against oracle of 14.1b and baseline of 17.3b

bsearch94.0ms

Steps

Iters	Range		Point
8	-7.171553699074835e+91	-1.194776095236265e+88	-7.011154002702933e+91
6	-7.828969379025143e+161	-1.2817277478091954e+161	-1.304579087607779e+161

simplify35.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

759.0ms

8412×

body

valid