Details

sample27.0ms

Algorithm

intervals

Results

10.0ms

276×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (* a c) (* b d))
29.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite65.0ms

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

Counts

2 → 47

Calls

2 calls:

14.0ms	(+ (* a c) (* b d))
49.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* a c) (* b d))
142.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.7s

Counts

53 → 53

Iterations

Useful iterations: 3 (569.0ms)

Iter	Nodes	Cost
0	89	972
1	245	818
2	833	759
3	2673	743
done	5000	743

prune198.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.2b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.3b	(fma a c (* b d))
17.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite57.0ms

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)
41.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
1.0ms	(fma a c (* b d))
9.0ms	(/ (fma a c (* b d)) (hypot c d))

series554.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(hypot c d)
280.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
58.0ms	(fma a c (* b d))
156.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.7s

Counts

119 → 119

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	146	1955
1	339	1821
2	1083	1579
3	4001	1579
done	5000	1546

prune344.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.3b	(fma a c (* b d))
17.5b	(/ (fma a c (* b d)) (hypot c d))

rewrite36.0ms

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)
18.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series372.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot c d)
133.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
41.0ms	(fma a c (* b d))
144.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify2.0s

Counts

133 → 133

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	167	2544
1	333	2481
2	714	2298
3	2050	2244
done	5000	2182

prune514.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.3b	(fma a c (* b d))
17.6b	(/ (hypot c d) (fma a c (* b d)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 319

Calls

4 calls:

26.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
10.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.0ms	(fma a c (* b d))
5.0ms	(/ (hypot c d) (fma a c (* b d)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
149.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
68.0ms	(fma a c (* b d))
137.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify1.3s

Counts

331 → 331

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	458	8797
1	1013	7708
2	1901	7150
done	5000	6968

prune601.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 6.1b

regimes275.0ms

Accuracy

33% (7.5b remaining)

Error of 13.3b against oracle of 5.8b and baseline of 17.0b

bsearch68.0ms

Steps

Iters	Range		Point
10	1.6535743575159948e+177	1.1864578754549863e+190	4.260571309999531e+183
7	-6.583000647768478e+110	-1.9941030622962047e+109	-4.583507366299893e+110

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	39
1	26	33
done	26	33

end0.0ms

sample612.0ms

Algorithm

intervals

Results

294.0ms

8487×

body

valid