Details

sample27.0ms

Algorithm

intervals

Results

13.0ms

275×

body

valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize16.0ms

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)))

rewrite28.0ms

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:

6.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (* b c) (* a d))
122.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify2.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	3648
2	798
1	218
0	86

prune430.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 24.2b

localize24.0ms

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)))

rewrite56.0ms

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:

13.0ms	(- (* b c) (* a d))
36.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
3.0ms	(sqrt (fma d d (* c c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* b c) (* a d))
179.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
60.0ms	(sqrt (fma d d (* c c)))
62.0ms	(sqrt (fma d d (* c c)))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1030
1	264
0	112

prune739.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize33.0ms

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)))

rewrite56.0ms

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:

17.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
14.0ms	(- (* b c) (* a d))
18.0ms	(/ (- (* b c) (* a d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
57.0ms	(- (* b c) (* a d))
143.0ms	(/ (- (* b c) (* a d)) (hypot d c))
57.0ms	(sqrt (fma d d (* c c)))

simplify1.3s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	2589
1	600
0	252

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize16.0ms

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))

rewrite52.0ms

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:

15.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
12.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series381.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
60.0ms	(- (* b c) (* a d))
147.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2285
1	475
0	185

prune744.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

regimes433.0ms

Accuracy

34% (7.3b remaining)

Error of 13.0b 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

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

861.0ms

8432×

body

valid