Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	197×	body	80	valid
27.0ms	20×	body	640	valid
11.0ms	256×	pre	80	true
11.0ms	16×	body	1280	valid
8.0ms	17×	body	320	valid
2.0ms	6×	body	160	valid

simplify824.0ms

Counts: 1 → 1

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize51.0ms

Local error

Found 3 expressions with local error:

1.5b	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.3b	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.3b	(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`distribute-lft-out--` `difference-of-squares` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `fma-udef` `flip--`

Counts

3 → 95

Calls

3 calls:

Slowest

40.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
12.0ms	(/ (- beta alpha) (fma 2 i (+ beta alpha)))
1.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series376.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

204.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
95.0ms	(/ (- beta alpha) (fma 2 i (+ beta alpha)))
77.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify1.7s

Counts: 104 → 104

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha)))) 1.0)
0.3b	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.2b	(/ 1 (fma 2 i (+ beta alpha)))
0.2b	(* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
36×	`times-frac`
30×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
10×	`distribute-lft-out`
7×	`pow1` `associate-/r` `associate-/l`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `flip3--` `1-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `flip-+` `flip--` `associate-/l/`
1×	`pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

Slowest

34.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
27.0ms	(* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha))))
4.0ms	(/ 1 (fma 2 i (+ beta alpha)))
1.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha)))) 1.0)

series577.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

218.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha)))) 1.0)
132.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
124.0ms	(* (- beta alpha) (/ 1 (fma 2 i (+ beta alpha))))
104.0ms	(/ 1 (fma 2 i (+ beta alpha)))

simplify2.7s

Counts: 145 → 145

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize43.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
1.5b	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.3b	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.3b	(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`times-frac`
25×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/l*`
8×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
3×	`log-prod`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `rem-log-exp` `log-pow` `fma-udef` `flip--`

Counts

4 → 110

Calls

4 calls:

Slowest

43.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
25.0ms	(/ (- beta alpha) (fma 2 i (+ beta alpha)))
2.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
0.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series794.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

360.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
182.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
134.0ms	(/ (- beta alpha) (fma 2 i (+ beta alpha)))
118.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

simplify1.5s

Counts: 122 → 122

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize64.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
2.8b	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
2.8b	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
1.5b	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `log-pow`
1×	`fma-udef`

Counts

4 → 56

Calls

4 calls:

Slowest

2.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
2.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
2.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
0.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

387.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
335.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
303.0ms	(log (fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0))
202.0ms	(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify854.0ms

Counts: 68 → 68

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.6b

regimes312.0ms

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch8.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	6365×	body	80	valid
408.0ms	552×	body	640	valid
389.0ms	8000×	pre	80	true
372.0ms	504×	body	1280	valid
184.0ms	373×	body	320	valid
77.0ms	206×	body	160	valid