Details

sample315.0ms

Algorithm

intervals

Results

71.0ms	368×	body	80	nan
16.0ms	157×	body	80	valid
16.0ms	29×	body	1280	nan
13.0ms	25×	body	1280	valid
12.0ms	31×	body	640	valid
10.0ms	31×	body	320	valid
9.0ms	22×	body	640	nan
6.0ms	17×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify4.3s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.4b

localize47.0ms

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)
13.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
20.9b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite197.0ms

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:

57.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
14.0ms	(* (sqrt 2) t)
57.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
64.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

535.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
60.0ms	(* (sqrt 2) t)
243.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1605
1	483
0	181

prune609.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize54.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
5.7b	(/ (* l l) x)
8.8b	(/ (* t t) x)
29.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

rewrite21.0ms

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

series380.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
27.0ms	(/ (* l l) x)
23.0ms	(/ (* t t) x)
242.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

simplify1.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5020
2	1498
1	356
0	134

prune596.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
8.8b	(/ (* t t) x)
29.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

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:

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

series406.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sqrt 2) t)
95.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
23.0ms	(/ (* t t) x)
213.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

simplify3.3s

Counts

88 → 88

Iterations

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

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize92.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
8.8b	(/ (* t t) x)
29.7b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
11×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

10.0ms	(* (cbrt x) (cbrt x))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
18.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

series711.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (cbrt x) (cbrt x))
111.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2)))
21.0ms	(/ (* t t) x)
234.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) 2))))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4758
2	1139
1	368
0	150

prune784.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

regimes941.0ms

Accuracy

74.3% (6.2b remaining)

Error of 10.2b against oracle of 4.1b and baseline of 28.0b

bsearch1.3s

Steps

Iters	Range		Point
5	1.3130252270366046e+71	4.433828109790897e+71	4.3628481786376754e+71
9	-7.865323649264117e-249	-2.5989217204882638e-256	-9.131577791002971e-250
8	-9.554269064230224e-225	-6.56997699479388e-228	-3.1340173156713147e-226
7	-8863632844576612.0	-362820003114431.56	-8781316784794473.0

simplify28.0ms

Iterations

Iter	Nodes
done	68
1	68
0	61

end0.0ms

sample5.8s

Algorithm

intervals

Results

1.4s	5137×	body	80	valid
1.4s	10359×	body	80	nan
552.0ms	848×	body	1280	valid
455.0ms	672×	body	320	valid
442.0ms	963×	body	640	valid
387.0ms	633×	body	1280	nan
276.0ms	623×	body	640	nan
156.0ms	380×	body	160	valid
140.0ms	348×	body	320	nan
34.0ms	183×	body	160	nan