Details

sample522.0ms

Algorithm

intervals

Results

83.0ms	31×	body	640	valid
74.0ms	341×	body	80	nan
73.0ms	164×	body	80	valid
56.0ms	26×	body	1280	valid
21.0ms	20×	body	1280	nan
20.0ms	23×	body	640	nan
15.0ms	23×	body	320	valid
6.0ms	12×	body	160	valid
5.0ms	9×	body	320	nan
2.0ms	6×	body	160	nan

simplify445.0ms

Counts: 1 → 1

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.0b

localize72.0ms

Local error

Found 4 expressions with local error:

20.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b	(* (sqrt 2) t)
0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

Slowest

66.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
50.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
39.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
8.0ms	(* (sqrt 2) t)

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
468.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
266.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
65.0ms	(* (sqrt 2) t)

simplify771.0ms

Counts: 120 → 106

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize46.0ms

Local error

Found 4 expressions with local error:

25.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
7.8b	(/ (* t t) x)
7.0b	(/ (* l l) (/ x 2))
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

Slowest

14.0ms	(/ (* t t) x)
11.0ms	(/ (* l l) (/ x 2))
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
113.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))
44.0ms	(/ (* l l) (/ x 2))
37.0ms	(/ (* t t) x)

simplify614.0ms

Counts: 131 → 112

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize46.0ms

Local error

Found 4 expressions with local error:

25.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
7.8b	(/ (* t t) x)
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
0.5b	(* (sqrt 2) t)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

Slowest

10.0ms	(/ (* t t) x)
8.0ms	(* (sqrt 2) t)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

372.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
183.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
58.0ms	(* (sqrt 2) t)
25.0ms	(/ (* t t) x)

simplify785.0ms

Counts: 94 → 88

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize56.0ms

Local error

Found 4 expressions with local error:

25.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l)))))
7.8b	(/ (* t t) x)
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l))))
0.5b	(* (sqrt 2) t)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

Slowest

9.0ms	(/ (* t t) x)
8.0ms	(* (sqrt 2) t)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l)))))
88.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ l (/ (/ x 2) l))))
56.0ms	(* (sqrt 2) t)
21.0ms	(/ (* t t) x)

simplify310.0ms

Counts: 94 → 88

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

regimes813.0ms

Accuracy

78% (5.2b remaining)

Error of 8.9b against oracle of 3.7b and baseline of 27.4b

bsearch1.0s

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.2s	10227×	body	80	nan
1.2s	612×	body	1280	nan
1.1s	5156×	body	80	valid
1.0s	1067×	body	640	valid
932.0ms	808×	body	1280	valid
612.0ms	324×	body	160	valid
500.0ms	591×	body	640	nan
436.0ms	645×	body	320	valid
246.0ms	323×	body	320	nan
53.0ms	148×	body	160	nan