Details

sample111.0ms

Algorithm

intervals

Results

46.0ms	273×	body	10240	exit
32.0ms	107×	body	1280	valid
12.0ms	67×	body	640	valid
4.0ms	42×	body	320	valid
2.0ms	25×	body	160	valid
1.0ms	15×	body	80	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 7 (44.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

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

series92.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
71.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify74.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343
done	5002	343

prune108.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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:

0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
5.0ms	(- x (* 1/3 (pow x 3)))
12.0ms	(* 1/3 (pow x 3))

series170.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms	(- x (* 1/3 (pow x 3)))
39.0ms	(* 1/3 (pow x 3))

simplify41.0ms

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5002	292
done	5002	292

prune159.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 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))
2.5b	(exp (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

6.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
12.0ms	(* 1/3 (pow x 3))
3.0ms	(exp (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

series222.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- x (* 1/3 (pow x 3)))
55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
35.0ms	(* 1/3 (pow x 3))
54.0ms	(exp (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

simplify37.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	237	493
1	894	432
2	5002	419
done	5002	419

prune204.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 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))
2.6b	(pow E (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
10×	`add-exp-log`
7×	`unpow-prod-down`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `pow-unpow` `cube-prod` `log1p-expm1-u` `unswap-sqr`
3×	`unpow-prod-up` `log-prod` `fma-neg` `associate-l` `prod-diff` `pow-exp` `prod-exp` `sqr-pow`
2×	`pow-to-exp`
1×	`cube-mult` `sub-neg` `e-exp-1` `flip3--` `pow-pow` `diff-log` `unpow3` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

4 → 87

Calls

4 calls:

5.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
12.0ms	(* 1/3 (pow x 3))
3.0ms	(pow E (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- x (* 1/3 (pow x 3)))
50.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
41.0ms	(* 1/3 (pow x 3))
168.0ms	(pow E (log (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

simplify49.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	358	642
1	1426	584
2	5001	568
done	5001	568

prune237.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes20.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	13	6
2	13	6
done	13	6

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7571×	body	10240	exit
975.0ms	3340×	body	1280	valid
440.0ms	2485×	body	640	valid
132.0ms	1168×	body	320	valid
40.0ms	601×	body	160	valid
14.0ms	406×	body	80	valid