Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

259×

body

valid

simplify114.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize24.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (* b c) (* a d))
25.3b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite77.0ms

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:

16.0ms	(- (* b c) (* a d))
60.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (* b c) (* a d))
126.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify787.0ms

Counts

56 → 56

Iterations

Useful iterations: done (785.0ms)

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

prune253.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.2b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.5b	(fma b c (- (* d a)))
15.2b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot c d)
30.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms	(fma b c (- (* d a)))
5.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series559.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot c d)
242.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
58.0ms	(fma b c (- (* d a)))
195.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify2.3s

Counts

119 → 119

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	147	2085
1	400	2033
2	2265	1702
done	5001	1694

prune479.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma c b (* (- a) d)) (hypot c d)) (hypot c d))
0.5b	(fma c b (* (- a) d))
15.2b	(/ (fma c b (* (- a) d)) (hypot c d))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
17.0ms	(/ (/ (fma c b (* (- a) d)) (hypot c d)) (hypot c d))
1.0ms	(fma c b (* (- a) d))
14.0ms	(/ (fma c b (* (- a) d)) (hypot c d))

series445.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(hypot c d)
163.0ms	(/ (/ (fma c b (* (- a) d)) (hypot c d)) (hypot c d))
60.0ms	(fma c b (* (- a) d))
154.0ms	(/ (fma c b (* (- a) d)) (hypot c d))

simplify859.0ms

Counts

133 → 133

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	170	2712
1	356	2650
2	1608	2463
done	5000	2413

prune547.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.2b	(* (/ 1 (hypot c d)) (/ (fma b c (* (- a) d)) (hypot c d)))
0.5b	(fma b c (* (- a) d))
15.2b	(/ (fma b c (* (- a) d)) (hypot c d))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot c d)
29.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (* (- a) d)) (hypot c d)))
0.0ms	(fma b c (* (- a) d))
5.0ms	(/ (fma b c (* (- a) d)) (hypot c d))

series504.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(hypot c d)
220.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (* (- a) d)) (hypot c d)))
51.0ms	(fma b c (* (- a) d))
177.0ms	(/ (fma b c (* (- a) d)) (hypot c d))

simplify2.9s

Counts

119 → 119

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	148	2085
1	390	1972
2	2609	1702
done	5000	1694

prune401.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

regimes276.0ms

Accuracy

34.7% (7.0b remaining)

Error of 12.8b against oracle of 5.8b and baseline of 16.6b

bsearch65.0ms

Steps

Iters	Range		Point
7	1.1507004734249195e+75	6.28375514977393e+76	6.152282888480768e+76
7	-9.986183728447351e+162	-4.4878019732439455e+160	-1.5651675657811871e+162

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	34
1	23	34
2	27	34
3	28	34
done	28	34

end0.0ms

sample1.2s

Algorithm

intervals

Results

600.0ms

8444×

body

valid