Details

sample66.0ms

Algorithm

intervals

Results

16.0ms	192×	body	80	valid
14.0ms	26×	body	2560	valid
8.0ms	256×	pre	80	true
8.0ms	18×	body	1280	valid
3.0ms	10×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify151.0ms

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize49.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (+ (* (* 4 p) p) (* x x)))
0.7b	(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
0.0b	(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4 p) p) (* x x))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

Slowest

50.0ms	(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
45.0ms	(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
35.0ms	(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
22.0ms	(sqrt (+ (* (* 4 p) p) (* x x)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

282.0ms	(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
105.0ms	(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
80.0ms	(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
48.0ms	(sqrt (+ (* (* 4 p) p) (* x x)))

simplify1.1s

Counts: 108 → 108

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize40.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (fma 4 (* p p) (* x x)))
3.6b	(+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))
0.2b	(* x (/ 1 (sqrt (fma 4 (* p p) (* x x)))))
0.0b	(sqrt (* 0.5 (+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-l` `associate-*r/`
2×	`flip3-+` `pow1/2` `sqrt-div` `div-exp` `pow-prod-down` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `1-exp` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

Slowest

11.0ms	(* x (/ 1 (sqrt (fma 4 (* p p) (* x x)))))
8.0ms	(sqrt (* 0.5 (+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))))
5.0ms	(+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))
1.0ms	(sqrt (fma 4 (* p p) (* x x)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

274.0ms	(sqrt (* 0.5 (+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))))
115.0ms	(+ 1 (* x (/ 1 (sqrt (fma 4 (* p p) (* x x))))))
77.0ms	(* x (/ 1 (sqrt (fma 4 (* p p) (* x x)))))
72.0ms	(sqrt (fma 4 (* p p) (* x x)))

simplify953.0ms

Counts: 111 → 111

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize36.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (fma (* p p) 4 (* x x)))
14.5b	(sqrt (fma (* p p) 4 (* x x)))
14.5b	(sqrt (fma (* p p) 4 (* x x)))
0.7b	(+ (/ x (sqrt (fma (* p p) 4 (* x x)))) 1)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`fma-def` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

Slowest

12.0ms	(+ (/ x (sqrt (fma (* p p) 4 (* x x)))) 1)
2.0ms	(sqrt (fma (* p p) 4 (* x x)))
1.0ms	(sqrt (fma (* p p) 4 (* x x)))
1.0ms	(sqrt (fma (* p p) 4 (* x x)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(+ (/ x (sqrt (fma (* p p) 4 (* x x)))) 1)
72.0ms	(sqrt (fma (* p p) 4 (* x x)))
68.0ms	(sqrt (fma (* p p) 4 (* x x)))
53.0ms	(sqrt (fma (* p p) 4 (* x x)))

simplify2.5s

Counts: 97 → 97

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.5b

localize50.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (fma (* p p) 4 (* x x)))
14.5b	(sqrt (fma (* p p) 4 (* x x)))
14.5b	(sqrt (fma (* p p) 4 (* x x)))
4.4b	(* (* x x) (/ x (fma (* p p) 4 (* x x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-r`
12×	`pow1`
10×	`times-frac`
9×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`cbrt-undiv` `div-exp` `unswap-sqr`
1×	`associate-l` `associate-r/` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

Slowest

28.0ms	(* (* x x) (/ x (fma (* p p) 4 (* x x))))
2.0ms	(sqrt (fma (* p p) 4 (* x x)))
2.0ms	(sqrt (fma (* p p) 4 (* x x)))
2.0ms	(sqrt (fma (* p p) 4 (* x x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

76.0ms	(* (* x x) (/ x (fma (* p p) 4 (* x x))))
66.0ms	(sqrt (fma (* p p) 4 (* x x)))
57.0ms	(sqrt (fma (* p p) 4 (* x x)))
57.0ms	(sqrt (fma (* p p) 4 (* x x)))

simplify1.1s

Counts: 98 → 98

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.5b

regimes177.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch6.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

835.0ms	651×	body	1280	valid
815.0ms	5951×	body	80	valid
658.0ms	774×	body	2560	valid
362.0ms	8000×	pre	80	true
164.0ms	336×	body	640	valid
56.0ms	63×	body	5120	valid
54.0ms	157×	body	320	valid
15.0ms	68×	body	160	valid