Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

273×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7
done	21	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
25.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite51.0ms

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:

8.0ms	(+ (* c c) (* d d))
8.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
36.0ms	(+ (* a c) (* b d))
88.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify133.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	290	532
1	1199	475
2	4872	462
3	5001	462
done	5001	462

prune202.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.5b	(fma a c (* b d))
17.9b	(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-exp-log`
86×	`prod-exp`
57×	`div-exp`
44×	`add-cbrt-cube`
35×	`1-exp`
16×	`cbrt-unprod`
14×	`cbrt-undiv`
12×	`rec-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`associate-r` `associate-l`
5×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `fma-udef` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

50.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms	(fma a c (* b d))
8.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

series355.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
41.0ms	(fma a c (* b d))
126.0ms	(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify47.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	472	1079
1	1607	796
2	5001	794
done	5001	794

prune226.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.5b	(fma a c (* b d))
17.9b	(/ (fma a c (* b d)) (hypot c d))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

14.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms	(fma a c (* b d))
7.0ms	(/ (fma a c (* b d)) (hypot c d))

series296.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
42.0ms	(fma a c (* b d))
124.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	297	767
1	1133	677
2	3251	677
3	5001	670
done	5001	670

prune275.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
0.5b	(fma a c (* b d))
18.0b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
29×	`add-cbrt-cube`
26×	`prod-exp`
23×	`div-exp`
18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `times-frac`
11×	`add-cube-cbrt`
9×	`cbrt-undiv` `1-exp` `cbrt-unprod`
5×	`pow1`
4×	`rec-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `fma-udef` `associate-/l*`

Counts

3 → 86

Calls

3 calls:

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

series299.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (* (hypot c d) 1))
46.0ms	(fma a c (* b d))
126.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify44.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	385	730
1	1623	579
2	5001	550
done	5001	550

prune184.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.5b

regimes231.0ms

Accuracy

24.7% (8.2b remaining)

Error of 13.6b against oracle of 5.5b and baseline of 16.3b

bsearch51.0ms

Steps

Iters	Range		Point
7	1.3381238936583669e+69	2.3069922374741435e+70	2.2847758660481544e+70
6	-7.922501144416864e+66	-5.906598016548616e+65	-7.723814496095852e+66

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	30	14
2	30	14
done	30	14

end0.0ms

sample569.0ms

Algorithm

intervals

Results

285.0ms

8463×

body

valid