Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

262×

body

valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
21.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

17.0ms	(+ (* c c) (* d d))
17.0ms	(+ (* a c) (* b d))
80.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* c c) (* d d))
64.0ms	(+ (* a c) (* b d))
148.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: 2 (304.0ms)

Iter	Nodes	Cost
0	104	1154
1	307	970
2	1451	867
done	5000	867

prune326.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.9b

localize13.0ms

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)) (hypot c d)))
0.8b	(fma a c (* b d))
14.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite58.0ms

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×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

6.0ms	(/ 1 (hypot c d))
42.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.0ms	(fma a c (* b d))
6.0ms	(/ (fma a c (* b d)) (hypot c d))

series604.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (hypot c d))
303.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
71.0ms	(fma a c (* b d))
171.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify2.4s

Counts

142 → 142

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	153	2192
1	404	2083
2	3047	1777
done	5000	1759

prune553.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.8b	(fma a c (* b d))
14.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite22.0ms

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 a c (* b d)) (hypot c d)) (hypot c d))
0.0ms	(fma a c (* b d))
6.0ms	(/ (fma a c (* b d)) (hypot c d))

series416.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
65.0ms	(fma a c (* b d))
185.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	160	2484
1	350	2423
2	1644	2254
done	5000	2206

prune536.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.0b	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.8b	(fma a c (* b d))
14.6b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite42.0ms

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*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 110

Calls

4 calls:

6.0ms	(/ 1 (hypot c d))
15.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.0ms	(fma a c (* b d))
18.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ 1 (hypot c d))
183.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
46.0ms	(fma a c (* b d))
148.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify1.2s

Counts

122 → 122

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	132	1652
1	304	1446
2	1977	1222
done	5000	1212

prune301.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

regimes267.0ms

Accuracy

33% (7.5b remaining)

Error of 13.2b against oracle of 5.7b and baseline of 16.9b

bsearch82.0ms

Steps

Iters	Range		Point
9	2.7695107245953193e+133	1.7651294170037398e+141	1.897415265281476e+140
5	-6.739608589523894e+87	-1.854378989895216e+87	-6.6258700830785885e+87

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	25	35
done	25	35

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8441×

body

valid