Details

sample423.0ms

Algorithm

intervals

Results

112.0ms	355×	body	80	nan
32.0ms	168×	body	80	valid
28.0ms	33×	body	640	valid
27.0ms	28×	body	1280	valid
19.0ms	19×	body	1280	nan
16.0ms	21×	body	640	nan
12.0ms	21×	body	320	valid
12.0ms	15×	body	320	nan
3.0ms	6×	body	160	valid
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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.4b

localize42.0ms

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))))
0.5b	(* (sqrt 2) t)
12.4b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
19.2b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite194.0ms

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)
31.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
54.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.2s

Counts

4 → 12

Calls

4 calls:

516.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
53.0ms	(* (sqrt 2) t)
250.0ms	(- (* (/ (+ 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)))

simplify11.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	7341
2	1684
1	466
0	181

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.2b

localize68.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma t t (/ l (/ x l)))
4.6b	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
9.4b	(/ (* t (* 4 t)) x)
26.9b	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

rewrite24.0ms

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))
20.0ms	(/ (* t (* 4 t)) x)
3.0ms	(sqrt (fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma t t (/ l (/ x l)))
93.0ms	(fma 2 (fma t t (/ l (/ x l))) (/ (* t (* 4 t)) x))
34.0ms	(/ (* t (* 4 t)) x)
340.0ms	(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

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize67.0ms

Local error

Found 4 expressions with local error:

26.9b	(sqrt (fma 2 (* (* (cbrt (fma t t (/ l (/ x l)))) (cbrt (fma t t (/ l (/ x l))))) (cbrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))
27.7b	(cbrt (fma t t (/ l (/ x l))))
27.7b	(cbrt (fma t t (/ l (/ x l))))
27.7b	(cbrt (fma t t (/ l (/ x l))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series822.0ms

Counts

4 → 12

Calls

4 calls:

386.0ms	(sqrt (fma 2 (* (* (cbrt (fma t t (/ l (/ x l)))) (cbrt (fma t t (/ l (/ x l))))) (cbrt (fma t t (/ l (/ x l))))) (/ (* t (* 4 t)) x)))
121.0ms	(cbrt (fma t t (/ l (/ x l))))
151.0ms	(cbrt (fma t t (/ l (/ x l))))
165.0ms	(cbrt (fma t t (/ l (/ x l))))

simplify3.0s

Counts

70 → 70

Iterations

Iter	Nodes
5	4261
4	1812
3	799
2	341
1	158
0	83

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize93.0ms

Local error

Found 4 expressions with local error:

27.7b	(cbrt (fma t t (/ l (/ x l))))
27.7b	(cbrt (fma t t (/ l (/ x l))))
27.7b	(cbrt (fma t t (/ l (/ x l))))
27.7b	(cbrt (fma t t (/ l (/ x l))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (fma t t (/ l (/ x l))))
3.0ms	(cbrt (fma t t (/ l (/ x l))))
2.0ms	(cbrt (fma t t (/ l (/ x l))))
2.0ms	(cbrt (fma t t (/ l (/ x l))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (fma t t (/ l (/ x l))))
150.0ms	(cbrt (fma t t (/ l (/ x l))))
156.0ms	(cbrt (fma t t (/ l (/ x l))))
136.0ms	(cbrt (fma t t (/ l (/ x l))))

simplify4.9s

Counts

68 → 68

Iterations

Iter	Nodes
6	5848
5	1691
4	686
3	326
2	145
1	79
0	46

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

regimes614.0ms

Accuracy

75.2% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 27.5b

bsearch1.8s

Steps

Iters	Range		Point
10	5.9175479702302504e+66	1.8619779487277368e+77	4.169836755076731e+68
9	2.180155274432473e-229	2.2769420534463193e-220	1.5173692864293495e-227
7	9.479799914111636e-251	2.4756009306801646e-249	1.0624147501299982e-249
9	-4.546275778593449e-29	-6.195157292696725e-35	-4.4981693604397794e-29

simplify55.0ms

Iterations

Iter	Nodes
4	68
3	68
2	65
1	62
0	51

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.2s	9936×	body	80	nan
1.4s	5080×	body	80	valid
980.0ms	826×	body	1280	valid
914.0ms	583×	body	640	nan
901.0ms	1022×	body	640	valid
780.0ms	644×	body	1280	nan
431.0ms	671×	body	320	valid
227.0ms	351×	body	320	nan
222.0ms	401×	body	160	valid
99.0ms	198×	body	160	nan