Details

sample28.0ms

Algorithm

intervals

Results

13.0ms

272×

body

valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	88	14
6	92	14
done	92	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
27.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite50.0ms

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

Counts

3 → 64

Calls

3 calls:

8.0ms	(+ (* c c) (* d d))
8.0ms	(- (* b c) (* a d))
32.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* c c) (* d d))
64.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	111	1202
1	312	1070
2	1052	961
3	3487	961
done	5000	960

prune259.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma b c (- (* d a)))
0.3b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
16.6b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite42.0ms

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:

0.0ms	(fma b c (- (* d a)))
31.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
7.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series474.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(fma b c (- (* d a)))
232.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
161.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify2.9s

Counts

106 → 106

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	140	2025
1	333	1894
2	1081	1642
3	4220	1642
done	5000	1608

prune338.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma b c (- (* d a)))
0.0b	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
16.6b	(/ (fma b c (- (* d a))) (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:

0.0ms	(fma b c (- (* d a)))
12.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
5.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series401.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(fma b c (- (* d a)))
171.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
159.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify1.8s

Counts

120 → 120

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	161	2652
1	327	2592
2	749	2403
3	2556	2349
done	5001	2285

prune365.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma b c (- (* d a)))
0.0b	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
16.7b	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

0.0ms	(fma b c (- (* d a)))
21.0ms	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
15.0ms	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

series355.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(fma b c (- (* d a)))
152.0ms	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
154.0ms	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

simplify2.4s

Counts

86 → 86

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	120	1449
1	272	1289
2	799	1059
3	3499	1045
done	5001	1044

prune191.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

regimes194.0ms

Accuracy

37% (7.0b remaining)

Error of 12.6b against oracle of 5.6b and baseline of 16.7b

bsearch80.0ms

Steps

Iters	Range		Point
9	1.5814553296019978e+194	7.10860021261402e+199	1.6082228280465774e+194
7	-1.5687549986519656e+132	-4.3271727545254867e+130	-5.0891457798304875e+131

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	40
1	34	34
2	40	34
done	40	34

end0.0ms

sample867.0ms

Algorithm

intervals

Results

534.0ms

8480×

body

valid