Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

266×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
24.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite41.0ms

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` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

8.0ms	(+ (* a c) (* b d))
32.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ (* a c) (* b d))
119.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify980.0ms

Counts

53 → 53

Iterations

Useful iterations: done (978.0ms)

Iter	Nodes	Cost
0	89	972
1	248	818
2	1044	749
done	5000	747

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.2b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
15.4b	(/ (fma a c (* b d)) (hypot c d))

rewrite66.0ms

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:

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

series579.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(fma a c (* b d))
307.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
200.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.9s

Counts

106 → 106

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	139	1895
1	373	1783
2	2784	1541
done	5000	1527

prune525.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d b (* c a))
0.0b	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
15.4b	(/ (fma d b (* c a)) (hypot c d))

rewrite42.0ms

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:

1.0ms	(fma d b (* c a))
22.0ms	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
11.0ms	(/ (fma d b (* c a)) (hypot c d))

series359.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma d b (* c a))
186.0ms	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
128.0ms	(/ (fma d b (* c a)) (hypot c d))

simplify1.3s

Counts

120 → 120

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	160	2484
1	351	2423
2	1665	2254
done	5000	2206

prune499.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d b (* c a))
0.0b	(/ (* (fma d b (* c a)) (/ 1 (hypot c d))) (hypot c d))
15.5b	(* (fma d b (* c a)) (/ 1 (hypot c d)))

rewrite33.0ms

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:

0.0ms	(fma d b (* c a))
14.0ms	(/ (* (fma d b (* c a)) (/ 1 (hypot c d))) (hypot c d))
16.0ms	(* (fma d b (* c a)) (/ 1 (hypot c d)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma d b (* c a))
145.0ms	(/ (* (fma d b (* c a)) (/ 1 (hypot c d))) (hypot c d))
120.0ms	(* (fma d b (* c a)) (/ 1 (hypot c d)))

simplify1.2s

Counts

86 → 86

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	119	1355
1	289	1194
2	1743	994
done	5001	984

prune317.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.2b

regimes272.0ms

Accuracy

24.3% (10.9b remaining)

Error of 13.4b against oracle of 2.4b and baseline of 16.9b

bsearch245.0ms

Steps

Iters	Range		Point
9	1.2564916464665883e+128	1.0940963542127011e+133	1.0484121450209069e+133
9	4.62518452031582e-213	7.833661410696538e-206	4.694847582105376e-213
8	1.1699336559244646e-236	7.187404175808244e-234	6.370255659610306e-234
8	-5.1848556793692505e+109	-3.3364575624134836e+106	-3.114802040969311e+109

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	74
1	36	60
2	37	60
done	37	60

end0.0ms

sample1.1s

Algorithm

intervals

Results

650.0ms

8411×

body

valid