Details

sample35.0ms

Algorithm

intervals

Results

20.0ms

267×

body

valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	90	14
6	94	14
done	94	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* b c) (* a d))
25.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite64.0ms

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

Counts

2 → 50

Calls

2 calls:

17.0ms	(- (* b c) (* a d))
44.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series259.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (* b c) (* a d))
178.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify893.0ms

Counts

56 → 56

Iterations

Useful iterations: done (890.0ms)

Iter	Nodes	Cost
0	96	1020
1	275	919
2	1118	843
done	5000	841

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.3b	(fma b c (- (* d a)))
16.2b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite68.0ms

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:

49.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
1.0ms	(fma b c (- (* d a)))
10.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series585.0ms

Counts

3 → 9

Calls

3 calls:

312.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
64.0ms	(fma b c (- (* d a)))
208.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify2.0s

Counts

106 → 106

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	140	2025
1	389	1975
2	2089	1646
done	5001	1642

prune490.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
16.2b	(/ (fma a (- d) (* c b)) (hypot c d))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 101

Calls

2 calls:

11.0ms	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
20.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

series421.0ms

Counts

2 → 6

Calls

2 calls:

206.0ms	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
214.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

simplify933.0ms

Counts

107 → 107

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	155	2536
1	343	2477
2	1599	2310
done	5002	2268

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ 1 (/ (hypot c d) (fma a (- d) (* c b)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma a (- d) (* c b))))
16.2b	(/ (hypot c d) (fma a (- d) (* c b)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
238×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
35×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
19×	`associate-/r*` `add-cbrt-cube`
10×	`cbrt-undiv`
5×	`associate-/r/`
4×	`pow1` `rec-exp` `1-exp`
3×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

3 → 309

Calls

3 calls:

41.0ms	(/ (/ 1 (/ (hypot c d) (fma a (- d) (* c b)))) (hypot c d))
28.0ms	(/ 1 (/ (hypot c d) (fma a (- d) (* c b))))
10.0ms	(/ (hypot c d) (fma a (- d) (* c b)))

series652.0ms

Counts

3 → 9

Calls

3 calls:

265.0ms	(/ (/ 1 (/ (hypot c d) (fma a (- d) (* c b)))) (hypot c d))
252.0ms	(/ 1 (/ (hypot c d) (fma a (- d) (* c b))))
134.0ms	(/ (hypot c d) (fma a (- d) (* c b)))

simplify1.1s

Counts

318 → 318

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	454	9184
1	1312	8350
done	5001	7836

prune960.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.4b

regimes253.0ms

Accuracy

29.8% (10.3b remaining)

Error of 12.5b against oracle of 2.2b and baseline of 16.9b

bsearch90.0ms

Steps

Iters	Range		Point
7	1.821547073792465e+115	6.050378771870372e+116	2.9468590428583657e+116
7	-1.5593098650405636e+174	-7.484363023265762e+171	-8.854189588374422e+171

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	34
1	21	34
done	21	34

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

8438×

body

valid