Details

sample61.0ms

Algorithm

intervals

Results

42.0ms

270×

body

valid

simplify57.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	80
5	80
4	76
3	56
2	40
1	21
0	11

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize18.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
25.2b	(/ (- (* 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--` `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:

16.0ms	(- (* b c) (* a d))
29.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series189.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (* b c) (* a d))
135.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify653.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2484
2	718
1	220
0	88

prune619.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.3b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.5b	(sqrt (fma d d (* c c)))
29.5b	(sqrt (fma d d (* c c)))

rewrite33.0ms

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)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b c) (* a d))
157.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
77.0ms	(sqrt (fma d d (* c c)))
61.0ms	(sqrt (fma d d (* c c)))

simplify585.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2185
2	779
1	266
0	115

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 23.2b

localize33.0ms

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))
16.3b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.5b	(sqrt (fma d d (* c c)))

rewrite51.0ms

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:

20.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
8.0ms	(- (* b c) (* a d))
17.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
56.0ms	(- (* b c) (* a d))
165.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
59.0ms	(sqrt (fma d d (* c c)))

simplify1.7s

Counts

201 → 201

Iterations

Iter	Nodes
3	6364
2	1668
1	611
0	257

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot d c))
0.1b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
0.5b	(- (* b c) (* a d))
16.4b	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r*` `add-log-exp` `associate-/l/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-l/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

5.0ms	(/ 1 (hypot d c))
42.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
16.0ms	(- (* b c) (* a d))
46.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1 (hypot d c))
140.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
54.0ms	(- (* b c) (* a d))
141.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

simplify3.0s

Counts

140 → 140

Iterations

Iter	Nodes
3	7551
2	1754
1	448
0	165

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes315.0ms

Accuracy

34.5% (7.4b remaining)

Error of 12.2b against oracle of 4.9b and baseline of 16.1b

bsearch109.0ms

Steps

Iters	Range		Point
10	2.0646135058263718e+160	4.947165806828693e+174	3.326984136021426e+169
7	-2.4471444152543263e+126	-8.221488516676519e+124	-1.7011328718966327e+126

simplify5.0ms

Iterations

Iter	Nodes
2	27
1	27
0	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8496×

body

valid