Details

sample476.0ms

Algorithm

intervals

Results

96.0ms	170×	body	80	valid
57.0ms	301×	body	80	nan
52.0ms	20×	body	1280	nan
30.0ms	30×	body	1280	valid
19.0ms	27×	body	640	valid
13.0ms	14×	body	640	nan
11.0ms	19×	body	320	valid
7.0ms	11×	body	320	nan
4.0ms	10×	body	160	valid
1.0ms	3×	body	160	nan

simplify1.9s

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.2b

localize62.0ms

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)
12.7b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
23.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite169.0ms

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:

68.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
8.0ms	(* (sqrt 2) t)
26.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
63.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

452.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
57.0ms	(* (sqrt 2) t)
268.0ms	(- (* (/ (+ 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)))

simplify11.3s

Counts

106 → 106

Iterations

Iter	Nodes
3	7341
2	1684
1	466
0	181

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.1b

localize54.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (/ l (/ x l)))
4.8b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
10.4b	(/ (* t (* 4 t)) x)
30.2b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite23.0ms

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))
19.0ms	(/ (* t (* 4 t)) x)
2.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma t t (/ l (/ x l)))
77.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
27.0ms	(/ (* t (* 4 t)) x)
346.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
3	4224
2	928
1	291
0	128

prune942.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.0b

localize70.0ms

Local error

Found 4 expressions with local error:

14.4b	(sqrt (* (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))) (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))))
31.1b	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
31.1b	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
31.1b	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 64

Calls

4 calls:

5.0ms	(sqrt (* (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))) (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))))
1.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
1.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
6.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series999.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(sqrt (* (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))) (cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))))
236.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
276.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
286.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
5	5093
4	1688
3	676
2	318
1	160
0	87

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.0b

localize126.0ms

Local error

Found 4 expressions with local error:

30.2b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
30.2b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
31.1b	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
31.1b	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
2.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
1.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
2.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
386.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
201.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))
230.0ms	(cbrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
4	2770
3	1057
2	446
1	193
0	93

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.0b

regimes759.0ms

Accuracy

78.5% (5.1b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.8b

bsearch1.9s

Steps

Iters	Range		Point
9	2.4705644922351665e+134	1.0317583027926416e+141	1.1429092917229189e+136
8	2.3578502464846e-162	1.1338586686334638e-159	1.351904254863679e-161
8	4.909230640994137e-244	6.457075559216039e-240	5.047696061686955e-240
10	-1.4127051641121057e-275	-9.154157246979375e-288	-3.737726633798208e-276
8	-8.464715529728638e-167	-8.94496705084197e-170	-1.8034323523291548e-167
8	-1.9308205073062745e+67	-1.8562285193930908e+64	-1.429472263354247e+67

simplify34.0ms

Iterations

Iter	Nodes
4	65
3	65
2	62
1	59
0	51

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.1s	10140×	body	80	nan
1.9s	600×	body	1280	nan
1.1s	5168×	body	80	valid
869.0ms	990×	body	640	valid
848.0ms	865×	body	1280	valid
557.0ms	593×	body	640	nan
380.0ms	621×	body	320	valid
198.0ms	387×	body	320	nan
147.0ms	177×	body	160	nan
143.0ms	356×	body	160	valid