Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

265×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
27.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite42.0ms

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:

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

series158.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(+ (* a c) (* b d))
116.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.2s

Counts

53 → 53

Iterations

Useful iterations: 3 (713.0ms)

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

prune250.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.6b

localize19.0ms

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))
16.2b	(/ (fma a c (* b d)) (hypot c d))

rewrite56.0ms

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)
42.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
0.0ms	(fma a c (* b d))
8.0ms	(/ (fma a c (* b d)) (hypot c d))

series553.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot c d)
269.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
58.0ms	(fma a c (* b d))
175.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.1s

Counts

119 → 119

Iterations

Useful iterations: done (3.1s)

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

prune492.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.3b	(fma a c (* b d))
16.2b	(/ (fma a c (* b d)) (hypot c d))

rewrite48.0ms

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)
29.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
1.0ms	(fma a c (* b d))
9.0ms	(/ (fma a c (* b d)) (hypot c d))

series366.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot c d)
136.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
43.0ms	(fma a c (* b d))
137.0ms	(/ (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

prune692.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.3b	(fma a c (* b d))
16.3b	(* (fma a c (* b d)) (/ 1 (hypot c d)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot c d)
30.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
0.0ms	(fma a c (* b d))
22.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot c d)
152.0ms	(/ (* (fma a c (* b d)) (/ 1 (hypot c d))) (hypot c d))
60.0ms	(fma a c (* b d))
150.0ms	(* (fma a c (* b d)) (/ 1 (hypot c d)))

simplify3.0s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	126	1415
1	278	1252
2	794	1032
3	3098	1018
done	5000	1018

prune300.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

regimes234.0ms

Accuracy

37.4% (6.7b remaining)

Error of 12.6b against oracle of 6.0b and baseline of 16.6b

bsearch103.0ms

Steps

Iters	Range		Point
7	5.026165092204197e+184	4.358401358984652e+186	1.5430679091287252e+185
9	-9.137650963602708e+166	-1.1971825537892871e+162	-5.286331128515371e+162

simplify13.0ms

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	25	57
1	32	45
2	33	39
3	37	33
done	37	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

736.0ms

8453×

body

valid