Details

sample53.0ms

Algorithm

intervals

Results

30.0ms

276×

body

valid

simplify72.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.7b	(- (* b c) (* a d))
25.7b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma d d (* c c))
7.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series256.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(fma d d (* c c))
75.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify2.5s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3472
2	853
1	230
0	95

prune531.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 25.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.2b	(sqrt (fma d d (* c c)))
31.2b	(sqrt (fma d d (* c c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 92

Calls

4 calls:

7.0ms	(- (* b c) (* a d))
23.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b c) (* a d))
170.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
68.0ms	(sqrt (fma d d (* c c)))
63.0ms	(sqrt (fma d d (* c c)))

simplify2.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	2178
2	760
1	264
0	112

prune864.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
16.2b	(* (- (* b c) (* a d)) (/ 1 (sqrt (fma d d (* c c)))))
31.2b	(sqrt (fma d d (* c c)))
31.2b	(sqrt (fma d d (* c c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`flip3--` `associate-l` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `cbrt-unprod` `fma-udef` `hypot-def`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

13.0ms	(- (* b c) (* a d))
35.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (fma d d (* c c)))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* b c) (* a d))
181.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (fma d d (* c c)))))
62.0ms	(sqrt (fma d d (* c c)))
77.0ms	(sqrt (fma d d (* c c)))

simplify3.3s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
3	3093
2	919
1	335
0	137

prune838.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
25.7b	(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite44.0ms

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

Counts

2 → 48

Calls

2 calls:

13.0ms	(- (* b c) (* a d))
29.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

series230.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (* b c) (* a d))
155.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	2495
2	715
1	218
0	86

prune276.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.0b

regimes354.0ms

Accuracy

-1.8% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch58.0ms

Steps

Iters	Range		Point
9	2.1675332614166088e+58	1.841919235217342e+66	1.9376700173410365e+62

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8474×

body

valid