Details

sample330.0ms

Algorithm

intervals

Results

107.0ms	299×	body	80	nan
22.0ms	168×	body	80	valid
15.0ms	24×	body	1280	valid
15.0ms	26×	body	640	valid
10.0ms	15×	body	1280	nan
10.0ms	19×	body	640	nan
8.0ms	20×	body	320	valid
7.0ms	18×	body	320	nan
5.0ms	18×	body	160	valid
2.0ms	8×	body	160	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	18	27
1	63	26
2	190	26
3	1101	26
done	5001	26

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
13.6b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.4b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `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` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

70.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
11.0ms	(* (sqrt 2.0) t)
50.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
67.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.5s

Counts

4 → 12

Calls

4 calls:

684.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
78.0ms	(* (sqrt 2.0) t)
389.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.3s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify3.8s

Counts

102 → 102

Iterations

Useful iterations: 1 (1.5s)

Iter	Nodes	Cost
0	179	2660
1	4671	2369
done	5000	2369

prune640.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize22.0ms

Local error

Found 4 expressions with local error:

5.2b	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow t 2) x)
6.7b	(/ (pow l 2) x)
29.0b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

1.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
28.0ms	(/ (pow t 2) x)
17.0ms	(/ (pow l 2) x)
3.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
27.0ms	(/ (pow t 2) x)
24.0ms	(/ (pow l 2) x)
427.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify1.7s

Counts

139 → 139

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	218	1816
done	5000	1605

prune892.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
5.2b	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sqrt 2.0) t)
100.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
37.0ms	(/ (pow t 2) x)
256.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	186	1525
done	5000	1350

prune772.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
5.2b	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
6.7b	(/ (pow t 2) x)
29.0b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

77.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
9.0ms	(/ (pow t 2) x)
2.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
107.0ms	(fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x))))
23.0ms	(/ (pow t 2) x)
220.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (fabs l) (/ (fabs l) x)) (* 4.0 (/ (pow t 2) x)))))

simplify1.4s

Counts

112 → 112

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	194	1786
done	5000	1602

prune666.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes625.0ms

Accuracy

75.5% (5.9b remaining)

Error of 9.6b against oracle of 3.8b and baseline of 27.8b

bsearch919.0ms

Steps

Iters	Range		Point
8	7.407251155982859e+145	4.879894848387411e+149	7.531239479384591e+145
6	-1.4231360660802614e-302	-2.7726430826687857e-303	-1.3597432496115356e-302
8	-2.3731648380204055e-262	-6.820981679032075e-265	-4.150104375191896e-264
9	-4.978593612221029e+24	-1.6476339207743873e+19	-8.925948169228506e+21

simplify14.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	53	208
1	61	208
done	61	208

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.5s	10248×	body	80	nan
1.1s	1001×	body	640	valid
914.0ms	851×	body	1280	valid
672.0ms	5159×	body	80	valid
555.0ms	334×	body	320	nan
377.0ms	576×	body	1280	nan
366.0ms	635×	body	320	valid
289.0ms	591×	body	640	nan
71.0ms	354×	body	160	valid
34.0ms	180×	body	160	nan