Details

sample184.0ms

Algorithm

intervals

Results

36.0ms	18×	body	320	valid
29.0ms	354×	body	80	nan
15.0ms	181×	body	80	valid
12.0ms	34×	body	640	valid
8.0ms	18×	body	1280	nan
7.0ms	19×	body	1280	valid
4.0ms	17×	body	640	nan
3.0ms	12×	body	320	nan
1.0ms	9×	body	160	nan
1.0ms	4×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4592
5	1370
4	472
3	215
2	101
1	44
0	18

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
9.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
24.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite187.0ms

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:

68.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
18.0ms	(* (sqrt 2) t)
37.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
60.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

472.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
49.0ms	(* (sqrt 2) t)
300.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify2.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1605
1	483
0	181

prune738.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.4b

localize74.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
5.0b	(/ (* l l) x)
11.2b	(/ (* t t) x)
29.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
20.0ms	(/ (* l l) x)
22.0ms	(/ (* t t) x)
4.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
32.0ms	(/ (* l l) x)
34.0ms	(/ (* t t) x)
228.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5020
2	1498
1	356
0	134

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
11.2b	(/ (* t t) x)
29.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

rewrite44.0ms

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:

18.0ms	(* (sqrt 2) t)
1.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
20.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sqrt 2) t)
87.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
36.0ms	(/ (* t t) x)
234.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

simplify3.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4545
2	1019
1	317
0	132

prune600.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
4.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
11.2b	(/ (* t t) x)
29.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

47.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
10.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
110.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
22.0ms	(/ (* t t) x)
198.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5010
2	1243
1	340
0	138

prune528.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

regimes948.0ms

Accuracy

77.3% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.2b

bsearch1.7s

Steps

Iters	Range		Point
7	1.1309338413304086e+123	2.556259866195709e+124	1.4996133926227848e+124
11	2.7160922814063716e-171	2.320974549002931e-151	2.776222986329393e-161
9	2.7888354386856526e-229	2.5177007063076634e-220	1.1951227663536998e-222
9	-2.757932199019658e-244	-4.4129812563248435e-253	-1.8789547767602823e-244
5	-1.5326714186934164e-151	-6.409403706686988e-152	-6.488460202761919e-152
9	-1.1133318844274758e+103	-1.3138437013874411e+98	-1.235121765864116e+102

simplify61.0ms

Iterations

Iter	Nodes
done	79
1	79
0	67

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.5s	10084×	body	80	nan
1.4s	5177×	body	80	valid
767.0ms	576×	body	640	nan
516.0ms	961×	body	640	valid
497.0ms	866×	body	1280	valid
312.0ms	553×	body	1280	nan
306.0ms	662×	body	320	valid
204.0ms	357×	body	320	nan
81.0ms	190×	body	160	nan
73.0ms	334×	body	160	valid