Details

sample102.0ms

Algorithm

intervals

Results

39.0ms	232×	body	10240	exit
32.0ms	109×	body	1280	valid
15.0ms	83×	body	640	valid
4.0ms	39×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	12×	body	80	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (42.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite5.0ms

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:

1.0ms	(expm1 (+ x x))
1.0ms	(fma 1 1 (exp (+ x x)))
3.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series106.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(expm1 (+ x x))
25.0ms	(fma 1 1 (exp (+ x x)))
63.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify77.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (71.0ms)

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

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

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))

rewrite12.0ms

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:

1.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
3.0ms	(- x (* 1/3 (pow x 3)))
6.0ms	(* 1/3 (pow x 3))

series170.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune172.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
10×	`associate-l`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`prod-diff` `prod-exp`
5×	`associate-+r+`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `sqr-pow`
3×	`fma-neg`
2×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r-` `flip3--` `fma-def` `flip3-+` `unpow3` `flip--` `flip-+`

Counts

4 → 101

Calls

4 calls:

6.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
3.0ms	(- x (* 1/3 (pow x 3)))
5.0ms	(* (pow x 5) 2/15)
6.0ms	(* 1/3 (pow x 3))

series222.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
78.0ms	(- x (* 1/3 (pow x 3)))
52.0ms	(* (pow x 5) 2/15)
36.0ms	(* 1/3 (pow x 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	355	521
1	1456	467
2	5001	466

prune252.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(pow (cbrt x) 5)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
3.0ms	(pow (cbrt x) 5)

series790.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
183.0ms	(cbrt x)
177.0ms	(cbrt x)
251.0ms	(pow (cbrt x) 5)

simplify48.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	123	226
1	362	215
2	1302	206
3	5001	201

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

regimes20.0ms

Accuracy

0% (1.2b remaining)

Error of 1.9b against oracle of 0.7b and baseline of 1.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	29	14
2	29	14

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7440×	body	10240	exit
995.0ms	3332×	body	1280	valid
433.0ms	2442×	body	640	valid
128.0ms	1166×	body	320	valid
43.0ms	627×	body	160	valid
19.0ms	433×	body	80	valid