Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	51×	body	1280	valid
17.0ms	47×	body	640	valid
9.0ms	122×	body	80	valid
6.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2490
7	682
6	240
5	101
4	51
3	30
2	22
1	18
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
4.4b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
63×	`times-frac`
61×	`add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-exp-log`
5×	`flip3-+` `flip-+` `div-inv`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `expm1-def` `difference-of-sqr-1` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

2 → 132

Calls

2 calls:

21.0ms	(/ 2 (+ 1 (exp (* -2 x))))
63.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series129.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ 2 (+ 1 (exp (* -2 x))))
87.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.8s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
3	2451
2	948
1	397
0	172

prune484.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
17.2b	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/15 x)
32.0ms	(* (* x x) x)
1.0ms	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

series318.0ms

Counts

3 → 9

Calls

3 calls:

194.0ms	(fma (pow x 5) 2/15 x)
52.0ms	(* (* x x) x)
73.0ms	(fma -1/3 (* (* x x) x) (fma (pow x 5) 2/15 x))

simplify1.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5006
3	1700
2	388
1	136
0	70

prune293.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
0.7b	(log (exp (* (* x x) x)))
20.6b	(fma -1/3 (log (exp (* (* x x) x))) (fma (pow x 5) 2/15 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `pow-plus` `pow-prod-up` `add-cube-cbrt`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-r` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

0.0ms	(fma (pow x 5) 2/15 x)
24.0ms	(* (* x x) x)
4.0ms	(log (exp (* (* x x) x)))
0.0ms	(fma -1/3 (log (exp (* (* x x) x))) (fma (pow x 5) 2/15 x))

series334.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(fma (pow x 5) 2/15 x)
62.0ms	(* (* x x) x)
45.0ms	(log (exp (* (* x x) x)))
76.0ms	(fma -1/3 (log (exp (* (* x x) x))) (fma (pow x 5) 2/15 x))

simplify2.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5005
3	1521
2	419
1	161
0	90

prune363.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.7b	(log (sqrt (exp (* (* x x) x))))
0.7b	(log (sqrt (exp (* (* x x) x))))
20.6b	(fma -1/3 (+ (log (sqrt (exp (* (* x x) x)))) (log (sqrt (exp (* (* x x) x))))) (fma (pow x 5) 2/15 x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
12×	`log-prod`
11×	`add-exp-log`
10×	`add-sqr-sqrt` `log-pow`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`sqrt-pow1` `pow-plus` `pow-prod-up` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `exp-prod` `exp-to-pow` `pow1/2` `rem-log-exp` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

31.0ms	(* (* x x) x)
9.0ms	(log (sqrt (exp (* (* x x) x))))
16.0ms	(log (sqrt (exp (* (* x x) x))))
1.0ms	(fma -1/3 (+ (log (sqrt (exp (* (* x x) x)))) (log (sqrt (exp (* (* x x) x))))) (fma (pow x 5) 2/15 x))

series1.1s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x x) x)
480.0ms	(log (sqrt (exp (* (* x x) x))))
449.0ms	(log (sqrt (exp (* (* x x) x))))
148.0ms	(fma -1/3 (+ (log (sqrt (exp (* (* x x) x)))) (log (sqrt (exp (* (* x x) x))))) (fma (pow x 5) 2/15 x))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5004
3	1400
2	442
1	182
0	98

prune498.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch114.0ms

Steps

Iters	Range		Point
10	0.006928851504795399	801012902.7811656	0.006998885945432241
7	-0.3435485504518341	-0.0018335887134067947	-0.00838956395365049

simplify4.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	1674×	body	1280	valid
537.0ms	1231×	body	640	valid
319.0ms	4175×	body	80	valid
180.0ms	634×	body	320	valid
47.0ms	286×	body	160	valid