Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	81×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	158×	body	80	valid
3.0ms	40×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize4.0ms

Local error

Found 1 expressions with local error:

2.5b	(- (exp x) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(- (exp x) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	140	205
1	403	130
2	2063	120
3	5003	90

prune56.0ms

Filtered

31 candidates to 18 candidates (58.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
1.6b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
11.8b	(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-exp-log` `add-cbrt-cube`
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:

1.0ms	(fma 1/6 (pow x 3) x)
3.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series155.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(fma 1/6 (pow x 3) x)
46.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
31.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify88.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	140	391
1	510	356
2	2915	356
3	5002	356

prune157.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

11.8b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
13.1b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
13.1b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
13.1b	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
60.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
64.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
64.0ms	(cbrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	145	578
1	408	536
2	1953	530
3	5001	530

prune268.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
2.5b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `fma-udef` `div-inv`

Counts

3 → 62

Calls

3 calls:

4.0ms	(+ (exp x) 1.0)
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series123.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (exp x) 1.0)
69.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	217	568
1	607	522
2	2817	511
3	5003	511

prune170.0ms

Filtered

71 candidates to 56 candidates (78.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch39.0ms

Steps

Iters	Range		Point
9	-0.0004106978961831668	-2.2963680336716634e-10	-0.00011982150581412934

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms

sample867.0ms

Algorithm

intervals

Results

382.0ms	2227×	body	1280	valid
178.0ms	1711×	body	640	valid
101.0ms	5519×	body	80	valid
55.0ms	818×	body	320	valid
17.0ms	392×	body	160	valid