Details

sample120.0ms

Algorithm

intervals

Results

33.0ms	23×	body	2560	valid
26.0ms	191×	body	80	valid
16.0ms	20×	body	1280	valid
12.0ms	256×	pre	80	true
4.0ms	4×	body	5120	valid
3.0ms	7×	body	640	valid
2.0ms	6×	body	160	valid
2.0ms	5×	body	320	valid

simplify98.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

97.0ms

(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize43.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma p (* 4 p) (* x x)))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0b	(fma p (* 4 p) (* x x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 80

Calls

4 calls:

Slowest

9.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma p (* 4 p) (* x x))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
96.0ms	(sqrt (fma p (* 4 p) (* x x)))
68.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
55.0ms	(fma p (* 4 p) (* x x))

simplify1.8s

Counts

63 → 92

Calls

63 calls:

Slowest

281.0ms	(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
63.0ms	(/ (* (cbrt x) (cbrt x)) (* (cbrt (sqrt (fma p (* 4 p) (* x x)))) (cbrt (sqrt (fma p (* 4 p) (* x x))))))
57.0ms	(/ (* (cbrt x) (cbrt x)) (sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x))))))
52.0ms	(/ (* (cbrt x) (cbrt x)) (sqrt (sqrt (fma p (* 4 p) (* x x)))))
48.0ms	(/ 1 (sqrt (sqrt (fma p (* 4 p) (* x x)))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

localize34.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma p (* 4 p) (* x x)))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.3b	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.1b	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `sqrt-prod`
2×	`log-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

Slowest

2.0ms	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series534.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

234.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
124.0ms	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
102.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
74.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.3s

Counts

29 → 72

Calls

29 calls:

Slowest

275.0ms	(- (+ (log 1.0) (* 2 (log (/ -1 x)))) (* 2 (log (/ -1 p))))
249.0ms	(exp (* (cbrt (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))) (cbrt (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))))
124.0ms	(exp (log (* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))))
117.0ms	(exp (sqrt (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
115.0ms	(exp (log (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.1b

localize58.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma p (* 4 p) (* x x)))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.3b	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.1b	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`log-prod` `add-exp-log`
4×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-up` `unpow-prod-down` `sqrt-prod`
2×	`pow-exp` `log-pow`
1×	`pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

Slowest

5.0ms	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
3.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series722.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

321.0ms	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
219.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
103.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
80.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify3.4s

Counts

33 → 79

Calls

33 calls:

Slowest

451.0ms	(pow E (log (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
440.0ms	(pow (* (cbrt E) (cbrt E)) (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
387.0ms	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
383.0ms	(pow E (log (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
373.0ms	(pow (sqrt E) (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.1b

localize92.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma p (* 4 p) (* x x)))
17.4b	(sqrt (fma p (* 4 p) (* x x)))
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma p (* 4 p) (* x x)))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series397.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
108.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
99.0ms	(sqrt (fma p (* 4 p) (* x x)))
64.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify185.0ms

Counts

22 → 66

Calls

22 calls:

Slowest

22.0ms	(sqrt (sqrt (fma p (* 4 p) (* x x))))
20.0ms	(sqrt (sqrt (fma p (* 4 p) (* x x))))
20.0ms	(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
20.0ms	(sqrt (* (cbrt (fma p (* 4 p) (* x x))) (cbrt (fma p (* 4 p) (* x x)))))
19.0ms	(sqrt (fma p (* 4 p) (* x x)))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 6.1b

regimes95.0ms

Accuracy

-4.7% (7.9b remaining)

Error of 13.6b against oracle of 5.7b and baseline of 13.2b

bsearch185.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

993.0ms	6032×	body	80	valid
908.0ms	640×	body	1280	valid
614.0ms	734×	body	2560	valid
434.0ms	8000×	pre	80	true
209.0ms	310×	body	640	valid
58.0ms	151×	body	320	valid
47.0ms	55×	body	5120	valid
20.0ms	78×	body	160	valid