Details

sample387.0ms

Algorithm

intervals

Results

60.0ms	42×	body	640	valid
57.0ms	321×	body	80	nan
29.0ms	162×	body	80	valid
18.0ms	18×	body	1280	nan
17.0ms	24×	body	640	nan
16.0ms	17×	body	1280	valid
14.0ms	27×	body	320	valid
4.0ms	9×	body	320	nan
3.0ms	8×	body	160	valid
2.0ms	7×	body	160	nan

simplify1.7s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize41.0ms

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)
12.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.5b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite185.0ms

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:

64.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
14.0ms	(* (sqrt 2) t)
25.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
79.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

394.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
67.0ms	(* (sqrt 2) t)
253.0ms	(- (* (/ (+ 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)))

simplify10.8s

Counts

106 → 106

Iterations

Iter	Nodes
3	7341
2	1684
1	466
0	181

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma t t (/ l (/ x l)))
4.2b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
13.5b	(/ (* t (* 4 t)) x)
27.5b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite22.0ms

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

series495.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(fma t t (/ l (/ x l)))
73.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
26.0ms	(/ (* t (* 4 t)) x)
336.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
3	4224
2	928
1	291
0	128

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize57.0ms

Local error

Found 4 expressions with local error:

13.5b	(/ (* t (* 4 t)) x)
27.5b	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))
27.7b	(sqrt (fma t t (/ l (/ x l))))
27.7b	(sqrt (fma t t (/ l (/ x l))))

rewrite44.0ms

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:

35.0ms	(/ (* t (* 4 t)) x)
2.0ms	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))
3.0ms	(sqrt (fma t t (/ l (/ x l))))
2.0ms	(sqrt (fma t t (/ l (/ x l))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* t (* 4 t)) x)
391.0ms	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))
115.0ms	(sqrt (fma t t (/ l (/ x l))))
145.0ms	(sqrt (fma t t (/ l (/ x l))))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	4125
2	921
1	289
0	125

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize70.0ms

Local error

Found 4 expressions with local error:

27.5b	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (* (sqrt (sqrt (fma t t (/ l (/ x l))))) (sqrt (sqrt (fma t t (/ l (/ x l))))))) (/ (* t (* 4 t)) x)))
27.7b	(sqrt (fma t t (/ l (/ x l))))
27.7b	(sqrt (fma t t (/ l (/ x l))))
27.7b	(sqrt (fma t t (/ l (/ x l))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

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

series682.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(sqrt (fma 2 (* (sqrt (fma t t (/ l (/ x l)))) (* (sqrt (sqrt (fma t t (/ l (/ x l))))) (sqrt (sqrt (fma t t (/ l (/ x l))))))) (/ (* t (* 4 t)) x)))
124.0ms	(sqrt (fma t t (/ l (/ x l))))
106.0ms	(sqrt (fma t t (/ l (/ x l))))
104.0ms	(sqrt (fma t t (/ l (/ x l))))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
5	3183
4	1487
3	672
2	304
1	139
0	70

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

regimes707.0ms

Accuracy

77.2% (5.3b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 27.2b

bsearch490.0ms

Steps

Iters	Range		Point
8	3.497382872215968e+81	1.6000133661041192e+84	4.8064993713964147e+83
8	-9.097297478766575e+61	-4.797907393882946e+57	-8.954275544416124e+61

simplify15.0ms

Iterations

Iter	Nodes
2	53
1	53
0	46

end0.0ms

sample9.1s

Algorithm

intervals

Results

2.6s	9928×	body	80	nan
1.2s	335×	body	320	nan
1.1s	5169×	body	80	valid
899.0ms	835×	body	1280	valid
825.0ms	1013×	body	640	valid
707.0ms	605×	body	1280	nan
625.0ms	629×	body	640	nan
367.0ms	621×	body	320	valid
163.0ms	362×	body	160	valid
64.0ms	174×	body	160	nan