Details

sample1.0s

Algorithm

intervals

Results

498.0ms	165×	body	80	valid
75.0ms	311×	body	80	nan
43.0ms	14×	body	1280	nan
22.0ms	34×	body	640	valid
20.0ms	28×	body	1280	valid
12.0ms	20×	body	640	nan
9.0ms	18×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	7×	body	320	nan
2.0ms	7×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize77.0ms

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))))
0.5b	(* (sqrt 2.0) t)
11.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite198.0ms

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` `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 → 90

Calls

4 calls:

89.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
19.0ms	(* (sqrt 2.0) t)
26.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
58.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

560.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
50.0ms	(* (sqrt 2.0) t)
317.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1672
1	471
0	178

prune850.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize31.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
4.5b	(/ (* l l) x)
9.9b	(/ (* t t) x)
29.8b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

rewrite20.0ms

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` `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 → 71

Calls

4 calls:

0.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
8.0ms	(/ (* l l) x)
8.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t))))
35.0ms	(/ (* l l) x)
32.0ms	(/ (* t t) x)
278.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ (* l l) x) (* t t)))))

simplify1.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
2	1490
1	354
0	131

prune632.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (/ l (/ x l)) (* t t))
3.8b	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t))))
9.9b	(/ (* t t) x)
29.8b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
44×	`fma-def`
43×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

47.0ms	(+ (/ l (/ x l)) (* t t))
0.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t))))
13.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (/ l (/ x l)) (* t t))
119.0ms	(fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t))))
22.0ms	(/ (* t t) x)
200.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (+ (/ l (/ x l)) (* t t)))))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5021
2	1308
1	335
0	122

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize75.0ms

Local error

Found 4 expressions with local error:

9.9b	(/ (* t t) x)
29.8b	(sqrt (+ (/ l (/ x l)) (* t t)))
29.8b	(sqrt (+ (/ l (/ x l)) (* t t)))
29.8b	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `times-frac` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
6×	`hypot-def`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

17.0ms	(/ (* t t) x)
87.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
84.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
2.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))

series732.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* t t) x)
228.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
230.0ms	(sqrt (+ (/ l (/ x l)) (* t t)))
251.0ms	(sqrt (fma 4.0 (/ (* t t) x) (* 2.0 (* (sqrt (+ (/ l (/ x l)) (* t t))) (sqrt (+ (/ l (/ x l)) (* t t)))))))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5009
2	1175
1	310
0	121

prune688.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

regimes1.1s

Accuracy

75.3% (5.9b remaining)

Error of 9.5b against oracle of 3.6b and baseline of 27.6b

bsearch720.0ms

Steps

Iters	Range		Point
8	1.5006603296515914e+61	3.0732393759999008e+65	2.4462062203769888e+64
7	-5.065066611154205e-207	-2.784466189462717e-208	-1.7671121844270954e-207
6	-1.7922940879838889e-177	-1.4018148741289176e-178	-5.242249805913046e-178
7	-59079395044398.75	-894857869810.5616	-58247696904127.21

simplify25.0ms

Iterations

Iter	Nodes
done	68
1	68
0	59

end0.0ms

sample5.9s

Algorithm

intervals

Results

1.3s	5150×	body	80	valid
1.0s	9831×	body	80	nan
958.0ms	867×	body	1280	valid
777.0ms	967×	body	640	valid
444.0ms	590×	body	1280	nan
254.0ms	617×	body	640	nan
235.0ms	673×	body	320	valid
115.0ms	203×	body	160	nan
79.0ms	322×	body	320	nan
65.0ms	343×	body	160	valid