Details

sample205.0ms

Algorithm

intervals

Results

64.0ms	85×	body	1280	valid
49.0ms	299×	body	80	valid
41.0ms	78×	body	640	valid
13.0ms	37×	body	320	valid
4.0ms	18×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	797
4	204
3	125
2	63
1	26
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp (- 0.0 im)) (exp im))
0.0b	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

14×	`fma-def` `*-un-lft-identity`
11×	`exp-sum`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`prod-diff`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`associate-r` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3-+` `associate-*r/` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 53

Calls

2 calls:

79.0ms	(+ (exp (- 0.0 im)) (exp im))
193.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

series187.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(+ (exp (- 0.0 im)) (exp im))
139.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))

simplify1.9s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
2	1632
1	291
0	97

prune445.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (sin re) (exp im))
0.0b	(fma (exp im) (sin re) (/ (sin re) (exp im)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

8.0ms	(/ (sin re) (exp im))
0.0ms	(fma (exp im) (sin re) (/ (sin re) (exp im)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (sin re) (exp im))
104.0ms	(fma (exp im) (sin re) (/ (sin re) (exp im)))

simplify1.7s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
3	2070
2	473
1	155
0	80

prune278.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp im) (exp im))
0.0b	(* (exp im) (exp im))
0.3b	(/ (* (* (sin re) 0.5) (fma (exp im) (* (exp im) (exp im)) (exp (fma 2 (- 0.0 im) (- 0.0 im))))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
5.0b	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
30×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
17×	`add-cbrt-cube`
13×	`add-exp-log`
8×	`exp-diff` `pow-prod-down` `associate-/r/` `pow-sqr` `pow-prod-up`
6×	`swap-sqr` `associate-r` `associate-l` `frac-add` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3-+` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 122

Calls

4 calls:

14.0ms	(* (exp im) (exp im))
18.0ms	(* (exp im) (exp im))
305.0ms	(/ (* (* (sin re) 0.5) (fma (exp im) (* (exp im) (exp im)) (exp (fma 2 (- 0.0 im) (- 0.0 im))))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
14.0ms	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (exp im) (exp im))
24.0ms	(* (exp im) (exp im))
388.0ms	(/ (* (* (sin re) 0.5) (fma (exp im) (* (exp im) (exp im)) (exp (fma 2 (- 0.0 im) (- 0.0 im))))) (+ (* (exp (- 0.0 im)) (exp (- 0.0 im))) (- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))))
79.0ms	(- (* (exp im) (exp im)) (* (exp (- 0.0 im)) (exp im)))

simplify3.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	4792
1	725
0	226

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))
0.0b	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
0.0b	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
0.3b	(* (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))

rewrite768.0ms

Algorithm

rewrite-expression-head

Rules

148×	`pow1`
80×	`pow-prod-down`
66×	`sqrt-pow1`
20×	`associate-*r/`
17×	`pow-prod-up`
16×	`sqrt-div`
14×	`pow1/2`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `pow-sqr`
9×	`flip3-+` `add-cube-cbrt` `flip-+`
8×	`associate-r`
6×	`sqrt-prod`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `swap-sqr` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`associate-l/` `-commutative`
1×	`pow2` `distribute-rgt-in` `rem-square-sqrt` `distribute-lft-in` `pow-plus` `sqrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

145.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))
58.0ms	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
68.0ms	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
487.0ms	(* (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))

series712.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))
212.0ms	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
194.0ms	(sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))
198.0ms	(* (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))) (sqrt (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im)))))

simplify2.8s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	2997
1	492
0	177

prune650.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes360.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.2s	3050×	body	1280	valid
1.8s	8522×	body	80	valid
1.5s	2621×	body	640	valid
500.0ms	1217×	body	320	valid
179.0ms	632×	body	160	valid