Details

sample314.0ms

Algorithm

intervals

Results

66.0ms	29×	body	640	valid
39.0ms	329×	body	80	nan
25.0ms	38×	body	1280	valid
18.0ms	158×	body	80	valid
10.0ms	21×	body	640	nan
10.0ms	19×	body	1280	nan
5.0ms	15×	body	320	valid
5.0ms	13×	body	320	nan
3.0ms	16×	body	160	valid
1.0ms	5×	body	160	nan

simplify6.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5010
7	2894
6	1606
5	890
4	445
3	209
2	98
1	41
0	18

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize162.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
15.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.2b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite511.0ms

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:

193.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
24.0ms	(* (sqrt 2.0) t)
122.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
160.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series4.0s

Counts

4 → 12

Calls

4 calls:

934.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
73.0ms	(* (sqrt 2.0) t)
578.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.4s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify4.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1721
1	476
0	182

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.4b

localize184.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
3.0b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
11.8b	(/ (* 4.0 (* t t)) x)
29.1b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-r*`
2×	`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 → 78

Calls

4 calls:

29.0ms	(* (sqrt 2.0) t)
2.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
81.0ms	(/ (* 4.0 (* t t)) x)
8.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sqrt 2.0) t)
178.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
41.0ms	(/ (* 4.0 (* t t)) x)
494.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify3.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1236
1	354
0	146

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize196.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.0b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
11.8b	(/ (* 4.0 (* t t)) x)
29.1b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

168.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
3.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
74.0ms	(/ (* 4.0 (* t t)) x)
4.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series777.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
138.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
47.0ms	(/ (* 4.0 (* t t)) x)
537.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify3.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1466
1	396
0	152

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.4b

localize236.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
3.0b	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
11.8b	(/ (* 4.0 (* t t)) x)
29.1b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

125.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
80.0ms	(/ (* 4.0 (* t t)) x)
9.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
163.0ms	(fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x)))
59.0ms	(/ (* 4.0 (* t t)) x)
884.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ l (/ x l)) (/ (* 4.0 (* t t)) x))))

simplify3.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1350
1	383
0	153

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

regimes1.9s

Accuracy

77.1% (5.4b remaining)

Error of 9.2b against oracle of 3.8b and baseline of 27.5b

bsearch916.0ms

Steps

Iters	Range		Point
6	9.653669233450707e+83	1.4909145897464132e+85	5.493219746550013e+84
6	6.61197000699045e-183	8.8917267424682e-182	3.1685097036544866e-182
9	2.8973638299661344e-272	1.3255921948966202e-266	1.311395206965946e-266
5	-5.038384936634917e+85	-1.5125315820373007e+85	-4.1438100975772846e+85

simplify74.0ms

Iterations

Iter	Nodes
done	61
1	61
0	51

end0.0ms

sample7.2s

Algorithm

intervals

Results

1.5s	10005×	body	80	nan
1.2s	5093×	body	80	valid
789.0ms	655×	body	320	valid
750.0ms	1011×	body	640	valid
740.0ms	877×	body	1280	valid
485.0ms	582×	body	1280	nan
352.0ms	606×	body	640	nan
250.0ms	330×	body	320	nan
94.0ms	364×	body	160	valid
42.0ms	166×	body	160	nan