Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	73×	body	1280	valid
6.0ms	54×	body	640	valid
2.0ms	89×	body	80	valid
2.0ms	26×	body	320	valid
2.0ms	88×	body	80	overflowed
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.1b	(- (exp x) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series40.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify189.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0b	(fma 1/6 (pow x 3) x)
14.1b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

3.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series135.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
71.0ms	(fma 1/6 (pow x 3) x)
26.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify94.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414

prune162.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
3.1b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
17×	`distribute-lft-out`
11×	`associate-/r/` `add-cbrt-cube`
9×	`add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 154

Calls

4 calls:

11.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.0ms	(+ (exp x) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
61.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	508	2170
1	2199	2059
2	5001	2056

prune411.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (exp x) 1.0))
3.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.1b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 46

Calls

4 calls:

3.0ms	(cbrt (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (+ (exp x) 1.0))
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
39.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	164	341
1	474	305
2	1812	301
3	5003	299

prune256.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

97.3% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 12.0b

bsearch42.0ms

Steps

Iters	Range		Point
9	-0.001787912586083248	-4.620053498493807e-09	-0.0001398161715025765

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	44
1	33	44

end0.0ms

sample888.0ms

Algorithm

intervals

Results

385.0ms	2229×	body	1280	valid
188.0ms	1721×	body	640	valid
56.0ms	2880×	body	80	valid
54.0ms	778×	body	320	valid
52.0ms	2550×	body	80	overflowed
18.0ms	394×	body	160	valid