Details

sample660.0ms

Algorithm

intervals

Results

210.0ms	357×	body	80	nan
85.0ms	28×	body	1280	valid
61.0ms	26×	body	320	valid
43.0ms	161×	body	80	valid
41.0ms	31×	body	1280	nan
35.0ms	30×	body	640	valid
24.0ms	23×	body	640	nan
7.0ms	7×	body	320	nan
5.0ms	11×	body	160	valid
1.0ms	2×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
6	2257
5	970
4	472
3	215
2	101
1	44
0	18

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
13.3b	(- (* (/ (+ 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)))

rewrite239.0ms

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:

89.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
58.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
73.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

506.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
78.0ms	(* (sqrt 2) t)
263.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.9s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify6.4s

Counts

106 → 106

Iterations

Iter	Nodes
3	8091
2	1703
1	467
0	181

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize53.0ms

Local error

Found 4 expressions with local error:

5.4b	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
7.8b	(/ x (* t t))
8.1b	(/ (* l l) x)
25.7b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
7.0ms	(/ x (* t t))
9.0ms	(/ (* l l) x)
1.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t))))
40.0ms	(/ x (* t t))
35.0ms	(/ (* l l) x)
397.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ 4 (/ x (* t t)))))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	3091
2	872
1	300
0	135

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
0.4b	(* (sqrt 2) t)
1.0b	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
25.7b	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

rewrite39.0ms

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*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`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 → 82

Calls

4 calls:

21.0ms	(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
14.0ms	(* (sqrt 2) t)
0.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
3.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

series841.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
69.0ms	(* (sqrt 2) t)
76.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
503.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

simplify1.6s

Counts

94 → 94

Iterations

Iter	Nodes
3	3662
2	858
1	289
0	133

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
0.5b	(* (* (sqrt 2) t) (/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))))
1.0b	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
25.7b	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

5.0ms	(/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
28.0ms	(* (* (sqrt 2) t) (/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))))
0.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
1.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

series910.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))))
185.0ms	(* (* (sqrt 2) t) (/ 1 (sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))))
117.0ms	(fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x))))
429.0ms	(sqrt (fma (/ l (/ x l)) 2 (* (* t t) (+ 2 (/ 4 x)))))

simplify2.2s

Counts

137 → 137

Iterations

Iter	Nodes
3	3804
2	1178
1	427
0	171

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes474.0ms

Accuracy

76.5% (5.5b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 27.1b

bsearch2.1s

Steps

Iters	Range		Point
8	1.6979862654485535e+131	3.234643949939514e+134	3.228763357777958e+132
10	1.783144167995163e-169	5.475896828624431e-155	4.752330698039452e-164
6	6.116042014021991e-195	5.396120080276413e-194	2.330241086706517e-194
10	-2.791851584579815e-267	-4.0855492648655506e-284	-4.983948587970619e-272
9	-2.3113061451997505e-162	-2.0386708656630003e-168	-1.5159399738466835e-163
6	-8.221488516676519e+124	-1.629530846283491e+124	-2.2951730784916024e+124

simplify52.0ms

Iterations

Iter	Nodes
2	66
1	66
0	55

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.1s	10045×	body	80	nan
1.4s	5067×	body	80	valid
1.2s	1040×	body	640	valid
1.1s	872×	body	1280	valid
670.0ms	589×	body	1280	nan
542.0ms	591×	body	640	nan
463.0ms	643×	body	320	valid
176.0ms	328×	body	320	nan
138.0ms	378×	body	160	valid
67.0ms	193×	body	160	nan