Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
21.0ms	228×	body	80	nan

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
2	32
1	27
0	18

prune59.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-/l`
1×	`pow2` `cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
9.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
16.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot re im)
505.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
258.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
219.0ms	(* (log base) (log base))

simplify2.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	2007
2	793
1	305
0	148

prune938.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
58×	`times-frac`
52×	`*-un-lft-identity`
42×	`add-cube-cbrt`
32×	`pow1`
30×	`associate-r` `associate-l` `add-exp-log`
29×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
12×	`log-prod` `swap-sqr` `log-pow`
10×	`prod-exp`
8×	`div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`frac-times` `associate-l/` `associate-r/` `fma-udef`

Counts

4 → 171

Calls

4 calls:

46.0ms	(* (/ 1 (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
13.0ms	(* (log base) (log base))
16.0ms	(* (log base) (log base))

series1.2s

Counts

4 → 12

Calls

4 calls:

467.0ms	(* (/ 1 (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))))
209.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
255.0ms	(* (log base) (log base))
249.0ms	(* (log base) (log base))

simplify3.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
3	4882
2	1729
1	597
0	215

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`pow1`
18×	`times-frac`
12×	`log-prod` `swap-sqr` `log-pow` `sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `associate-/r*` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))

series1.1s

Counts

4 → 12

Calls

4 calls:

462.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
219.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
217.0ms	(* (log base) (log base))
179.0ms	(* (log base) (log base))

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	1961
2	761
1	309
0	153

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))
0.6b	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
28×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`log-prod` `swap-sqr` `log-pow`
12×	`associate-r` `associate-l`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`pow3`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

14.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))
163.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

series845.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* (log base) (log base))
199.0ms	(* (log base) (log base))
218.0ms	(* (log base) (log base))
220.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

simplify2.2s

Counts

138 → 138

Iterations

Iter	Nodes
done	5002
4	1900
3	766
2	408
1	147
0	67

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes496.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.5s	7699×	body	80	nan