Details

sample105.0ms

Algorithm

intervals

Results

38.0ms	249×	body	10240	exit
34.0ms	108×	body	1280	valid
15.0ms	82×	body	640	valid
3.0ms	31×	body	320	valid
2.0ms	23×	body	160	valid
0.0ms	12×	body	80	valid

simplify47.0ms

Counts

1 → 1

Iterations

Useful iterations: 7 (45.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7
done	5001	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(expm1 (+ x x))
0.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
4×	`log1p-expm1-u`
3×	`pow1` `expm1-log1p-u` `associate-/r` `associate-/l` `add-log-exp`
2×	`expm1-udef`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

3 → 51

Calls

3 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
0.0ms	(expm1 (+ x x))
5.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series112.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
19.0ms	(expm1 (+ x x))
72.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify77.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382
done	5001	382

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (* 1/3 (pow x 3)))
0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b	(* 1/3 (pow x 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 63

Calls

3 calls:

8.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
13.0ms	(* 1/3 (pow x 3))

series170.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- x (* 1/3 (pow x 3)))
55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
36.0ms	(* 1/3 (pow x 3))

simplify34.0ms

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5001	292
done	5001	292

prune154.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 (exp x))
0.0b	(hypot 1 (exp x))
0.5b	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
1.0b	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`hypot-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `rem-square-sqrt` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

0.0ms	(hypot 1 (exp x))
0.0ms	(hypot 1 (exp x))
8.0ms	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
7.0ms	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot 1 (exp x))
54.0ms	(hypot 1 (exp x))
151.0ms	(/ (expm1 (+ x x)) (* (hypot 1 (exp x)) (hypot 1 (exp x))))
77.0ms	(* (hypot 1 (exp x)) (hypot 1 (exp x)))

simplify40.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	277	629
1	1300	519
2	5001	472
done	5001	472

prune184.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.7b	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
137.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
141.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
142.0ms	(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

simplify163.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	303	1267
1	1040	1174
2	4666	1078
3	5001	1030
done	5001	1030

prune299.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes25.0ms

Accuracy

0% (1.3b remaining)

Error of 1.9b against oracle of 0.6b and baseline of 1.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	5
1	18	5
2	18	5
done	18	5

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7579×	body	10240	exit
992.0ms	3301×	body	1280	valid
422.0ms	2424×	body	640	valid
142.0ms	1265×	body	320	valid
42.0ms	585×	body	160	valid
15.0ms	425×	body	80	valid