Details

sample322.0ms

Algorithm

intervals

Results

39.0ms	331×	body	80	nan
18.0ms	33×	body	1280	valid
17.0ms	161×	body	80	valid
12.0ms	20×	body	1280	nan
11.0ms	25×	body	640	valid
10.0ms	21×	body	640	nan
8.0ms	22×	body	320	valid
4.0ms	15×	body	160	valid
3.0ms	11×	body	320	nan
1.0ms	7×	body	160	nan

simplify4.2s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize82.0ms

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)
11.3b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite148.0ms

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:

49.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
29.0ms	(- (* (/ (+ 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)))

series2.3s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
73.0ms	(* (sqrt 2) t)
306.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify2.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1605
1	483
0	181

prune760.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.1b

localize67.0ms

Local error

Found 4 expressions with local error:

2.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
5.3b	(/ (* l l) x)
10.7b	(/ (* t t) x)
26.1b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

rewrite40.0ms

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

series376.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
23.0ms	(/ (* l l) x)
31.0ms	(/ (* t t) x)
238.0ms	(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

prune662.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
2.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
10.7b	(/ (* t t) x)
26.1b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

rewrite43.0ms

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:

15.0ms	(* (sqrt 2) t)
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
24.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sqrt 2) t)
115.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
40.0ms	(/ (* t t) x)
202.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4708
2	1019
1	319
0	132

prune652.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
2.8b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
10.7b	(/ (* t t) x)
26.1b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

rewrite63.0ms

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:

41.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
18.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
95.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
34.0ms	(/ (* t t) x)
216.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1220
1	342
0	138

prune577.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

regimes992.0ms

Accuracy

74.4% (6.2b remaining)

Error of 10.0b against oracle of 3.8b and baseline of 27.9b

bsearch1.8s

Steps

Iters	Range		Point
5	6.364793754454402e+60	1.7652923151240752e+61	8.400049024243972e+60
9	4.178826324149685e-184	4.985769453538649e-178	5.519300554524216e-179
10	-5.87551456151423e-303	2.02503051581541e-296	1.989394621889763e-296
9	-8.029424359520944e-243	-2.0952165801168822e-249	-7.929477479606887e-243
5	-1.82407131439873e-220	-6.727441174307589e-221	-9.825191585136072e-221
9	-1.454820351249388e+100	-1.197502721334482e+95	-1.91060683778735e+99

simplify54.0ms

Iterations

Iter	Nodes
done	63
1	63
0	55

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.3s	10063×	body	80	nan
1.1s	5088×	body	80	valid
1.1s	1061×	body	640	valid
678.0ms	616×	body	640	nan
501.0ms	624×	body	1280	nan
501.0ms	850×	body	1280	valid
244.0ms	639×	body	320	valid
99.0ms	310×	body	320	nan
81.0ms	362×	body	160	valid
76.0ms	189×	body	160	nan