Details

sample56.0ms

Algorithm

intervals

Results

39.0ms

267×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
24.1b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite40.0ms

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--` `insert-posit16` `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 → 50

Calls

2 calls:

8.0ms	(- (* b c) (* a d))
31.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series156.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (* b c) (* a d))
103.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify435.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
2	717
1	220
0	88

prune290.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
15.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.0b	(sqrt (fma d d (* c c)))
31.0b	(sqrt (fma d d (* c c)))

rewrite34.0ms

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:

8.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* 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)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b c) (* a d))
137.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
63.0ms	(sqrt (fma d d (* c c)))
52.0ms	(sqrt (fma d d (* c c)))

simplify502.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2001
2	778
1	266
0	115

prune644.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
0.5b	(- (* b c) (* a d))
15.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.0b	(sqrt (fma d d (* c c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `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 → 189

Calls

4 calls:

16.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
12.0ms	(- (* b c) (* a d))
17.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
45.0ms	(- (* b c) (* a d))
120.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
46.0ms	(sqrt (fma d d (* c c)))

simplify648.0ms

Counts

201 → 201

Iterations

Iter	Nodes
done	2003
2	1660
1	619
0	257

prune856.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
0.5b	(- (* c b) (* d a))
15.9b	(/ (- (* c b) (* d a)) (hypot d c))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

0.0ms	(hypot d c)
14.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
8.0ms	(- (* c b) (* d a))
17.0ms	(/ (- (* c b) (* d a)) (hypot d c))

series339.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot d c)
125.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
48.0ms	(- (* c b) (* d a))
113.0ms	(/ (- (* c b) (* d a)) (hypot d c))

simplify595.0ms

Counts

147 → 147

Iterations

Iter	Nodes
done	2019
2	1479
1	473
0	198

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

regimes268.0ms

Accuracy

34% (7.8b remaining)

Error of 13.0b against oracle of 5.3b and baseline of 17.0b

bsearch82.0ms

Steps

Iters	Range		Point
8	5.358739737127594e+138	3.125027152050763e+142	7.75132925369235e+139
6	-1.0929779358508971e+146	-8.954837193749603e+144	-6.603705426560988e+145

simplify3.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8493×

body

valid