Details

sample55.0ms

Algorithm

intervals

Results

23.0ms

275×

body

valid

simplify94.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize15.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (* b c) (* a d))
24.4b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite45.0ms

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` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `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

2 → 48

Calls

2 calls:

19.0ms	(- (* b c) (* a d))
24.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series198.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (* b c) (* a d))
130.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify2.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	2495
2	715
1	218
0	86

prune509.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.2b

localize45.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(sqrt (fma d d (* c c)))

rewrite40.0ms

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` `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 → 92

Calls

4 calls:

12.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* b c) (* a d))
178.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
76.0ms	(sqrt (fma d d (* c c)))
70.0ms	(sqrt (fma d d (* c c)))

simplify2.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	2178
2	760
1	264
0	112

prune769.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
1.1b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (hypot d c))
31.3b	(sqrt (fma d d (* c c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 179

Calls

4 calls:

34.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
14.0ms	(- (* b c) (* a d))
26.0ms	(/ (- (* b c) (* a d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
59.0ms	(- (* b c) (* a d))
165.0ms	(/ (- (* b c) (* a d)) (hypot d c))
54.0ms	(sqrt (fma d d (* c c)))

simplify1.4s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	1618
1	588
0	252

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
1.1b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 121

Calls

3 calls:

30.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
14.0ms	(- (* b c) (* a d))
24.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series380.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
73.0ms	(- (* b c) (* a d))
154.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1460
1	457
0	185

prune698.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

regimes473.0ms

Accuracy

34.1% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 16.7b

bsearch114.0ms

Steps

Iters	Range		Point
8	7.125568374099785e+144	5.300661243002492e+148	1.3360538186501758e+147
10	-1.1963497052112714e+106	-1.0713785531950437e+91	-1.477885392425796e+104

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

967.0ms

8432×

body

valid