Details

sample48.0ms

Algorithm

intervals

Results

22.0ms

265×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* a c) (* b d))
24.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite46.0ms

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

Counts

2 → 47

Calls

2 calls:

6.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series174.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (* a c) (* b d))
128.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.5s

Counts

53 → 53

Iterations

Useful iterations: 3 (770.0ms)

Iter	Nodes	Cost
0	87	972
1	243	818
2	864	747
3	3275	743
done	5000	743

prune305.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ 1 (hypot c 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))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `hypot-udef` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(hypot c d)
4.0ms	(/ 1 (hypot c d))
19.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series557.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot c d)
79.0ms	(/ 1 (hypot c d))
238.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
173.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.6s

Counts

142 → 142

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	2150
1	407	2041
2	2850	1735
done	5000	1723

prune515.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `clear-num` `frac-2neg`
1×	`associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(hypot c d)
9.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series365.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot c d)
49.0ms	(hypot c d)
132.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
133.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify568.0ms

Counts

133 → 133

Iterations

Useful iterations: done (564.0ms)

Iter	Nodes	Cost
0	161	2502
1	355	2439
2	1628	2270
done	5000	2228

prune612.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

196×	`times-frac`
151×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
104×	`add-exp-log` `add-cube-cbrt`
52×	`div-exp`
44×	`associate-r`
34×	`add-cbrt-cube`
28×	`prod-exp`
19×	`associate-/r*`
18×	`rec-exp` `1-exp`
15×	`unswap-sqr`
14×	`cbrt-undiv`
13×	`associate-l`
12×	`div-inv`
10×	`pow1`
9×	`associate-/l*`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-flip` `inv-pow` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`associate-/r/`
1×	`frac-times` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 263

Calls

4 calls:

4.0ms	(/ 1 (hypot c d))
8.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
41.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
4.0ms	(/ (hypot c d) (fma a c (* b d)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (hypot c d))
121.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
185.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
101.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify377.0ms

Counts

275 → 275

Iterations

Useful iterations: done (370.0ms)

Iter	Nodes	Cost
0	295	5558
1	964	4969
done	5001	4485

prune840.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes316.0ms

Accuracy

25% (7.9b remaining)

Error of 14.1b against oracle of 6.2b and baseline of 16.7b

bsearch172.0ms

Steps

Iters	Range		Point
8	1.8883840965187804e+99	7.38173445747568e+101	7.287774565713375e+101
7	-1.0095027531688244e+104	-1.7547760984372204e+102	-9.931482377190183e+103
9	-5.173593764286187e+189	-1.1912223558888474e+184	-4.928722227773501e+189
10	-9.616245507858335e+264	-1.2168755257065468e+252	-1.2360569206326496e+252

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	33	74
1	41	64
2	51	64
3	53	64
done	53	64

end0.0ms

sample1.1s

Algorithm

intervals

Results

744.0ms

8448×

body

valid