Details

sample320.0ms

Algorithm

intervals

Results

63.0ms	31×	body	1280	valid
56.0ms	347×	body	80	nan
34.0ms	9×	body	160	valid
28.0ms	38×	body	640	valid
26.0ms	161×	body	80	valid
16.0ms	18×	body	1280	nan
13.0ms	22×	body	640	nan
7.0ms	17×	body	320	valid
6.0ms	10×	body	320	nan
2.0ms	5×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	2403
5	990
4	463
3	210
2	99
1	42
0	18

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.7b

localize53.0ms

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)
15.2b	(- (* (/ (+ 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)))

rewrite200.0ms

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:

78.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
7.0ms	(* (sqrt 2) t)
39.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
72.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

503.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
78.0ms	(* (sqrt 2) t)
280.0ms	(- (* (/ (+ 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)))

simplify11.5s

Counts

106 → 106

Iterations

Iter	Nodes
3	7341
2	1684
1	466
0	181

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

localize63.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (/ l (/ x l)))
5.2b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
8.3b	(/ (* t (* 4 t)) x)
25.2b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

0.0ms	(fma t t (/ l (/ x l)))
0.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
35.0ms	(/ (* t (* 4 t)) x)
2.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma t t (/ l (/ x l)))
82.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
38.0ms	(/ (* t (* 4 t)) x)
351.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify2.1s

Counts

76 → 76

Iterations

Iter	Nodes
3	4224
2	928
1	291
0	128

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.6b

localize43.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (* t (* 4 t)) x)
25.2b	(sqrt (fma t t (/ l (/ x l))))
25.2b	(sqrt (fma t t (/ l (/ x l))))
25.2b	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

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

series633.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* t (* 4 t)) x)
99.0ms	(sqrt (fma t t (/ l (/ x l))))
102.0ms	(sqrt (fma t t (/ l (/ x l))))
398.0ms	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	3957
2	913
1	288
0	125

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* t 4) (/ t x))
0.4b	(* (sqrt 2) t)
5.2b	(fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x)))
25.2b	(sqrt (fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-r`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
9×	`times-frac`
7×	`associate-l` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `fma-udef` `div-inv`

Counts

4 → 88

Calls

4 calls:

40.0ms	(* (* t 4) (/ t x))
16.0ms	(* (sqrt 2) t)
0.0ms	(fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x)))
2.0ms	(sqrt (fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* t 4) (/ t x))
82.0ms	(* (sqrt 2) t)
108.0ms	(fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x)))
457.0ms	(sqrt (fma 2 (fma l (/ l x) (* t t)) (* (* t 4) (/ t x))))

simplify3.1s

Counts

100 → 100

Iterations

Iter	Nodes
3	5097
2	1287
1	407
0	161

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.6b

regimes652.0ms

Accuracy

78.2% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.7b

bsearch406.0ms

Steps

Iters	Range		Point
6	1.1534490798277808e+139	5.896067947804245e+139	4.088323180304518e+139
8	-2.771602622336687e+93	-5.381658407530287e+90	-2.661507795721962e+93

simplify16.0ms

Iterations

Iter	Nodes
2	52
1	52
0	44

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.0s	10466×	body	80	nan
1.6s	5143×	body	80	valid
1.0s	865×	body	1280	valid
899.0ms	1004×	body	640	valid
696.0ms	606×	body	1280	nan
473.0ms	624×	body	640	nan
329.0ms	640×	body	320	valid
172.0ms	338×	body	320	nan
154.0ms	348×	body	160	valid
65.0ms	197×	body	160	nan