Details

sample53.0ms

Algorithm

intervals

Results

24.0ms

273×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize29.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma a c (* b d))
27.0b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

1.0ms	(fma a c (* b d))
11.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series291.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(fma a c (* b d))
209.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify3.7s

Counts

45 → 45

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	64	725
1	102	714
2	263	622
3	957	622
4	4463	622
done	5000	622

prune489.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.8b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (hypot c d))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

51.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
1.0ms	(fma a c (* b d))
11.0ms	(/ (fma a c (* b d)) (hypot c d))

series674.0ms

Counts

3 → 9

Calls

3 calls:

358.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
75.0ms	(fma a c (* b d))
241.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify4.8s

Counts

106 → 106

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	139	1895
1	372	1783
2	2779	1541
done	5000	1527

prune752.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma c a (* b d)) (hypot c d)) (hypot c d))
0.8b	(fma c a (* b d))
16.3b	(/ (fma c a (* b d)) (hypot c d))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

12.0ms	(/ (/ (fma c a (* b d)) (hypot c d)) (hypot c d))
1.0ms	(fma c a (* b d))
10.0ms	(/ (fma c a (* b d)) (hypot c d))

series413.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(/ (/ (fma c a (* b d)) (hypot c d)) (hypot c d))
58.0ms	(fma c a (* b d))
176.0ms	(/ (fma c a (* b d)) (hypot c d))

simplify1.2s

Counts

120 → 120

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	161	2484
1	350	2423
2	1736	2254
done	5000	2212

prune852.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.5b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (fma c a (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.8b	(fma c a (* b d))
16.4b	(* (fma c a (* b d)) (/ 1 (hypot c d)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `associate-/l`

Counts

3 → 77

Calls

3 calls:

15.0ms	(/ (* (fma c a (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.0ms	(fma c a (* b d))
28.0ms	(* (fma c a (* b d)) (/ 1 (hypot c d)))

series494.0ms

Counts

3 → 9

Calls

3 calls:

220.0ms	(/ (* (fma c a (* b d)) (/ 1 (hypot c d))) (hypot c d))
85.0ms	(fma c a (* b d))
189.0ms	(* (fma c a (* b d)) (/ 1 (hypot c d)))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	120	1355
1	287	1194
2	1729	994
done	5001	994

prune486.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.5b

regimes585.0ms

Accuracy

15.9% (9.4b remaining)

Error of 15.2b against oracle of 5.8b and baseline of 17.0b

bsearch57.0ms

Steps

Iters	Range		Point
8	1.046808922065552e+119	3.7306603276180315e+121	2.0571322569994085e+121

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	25
1	19	25
done	19	25

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s

8471×

body

valid