Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	68×	body	1280	valid
7.0ms	60×	body	640	valid
3.0ms	161×	body	80	valid
2.0ms	31×	body	320	valid
1.0ms	19×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 42.9b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.7b	(- (exp x) 1.0)

rewrite6.0ms

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:

5.0ms

(- (exp x) 1.0)

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	137	205
1	379	130
2	1905	120
3	5001	90

prune47.0ms

Filtered

31 candidates to 18 candidates (41.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	3	32

Merged error: 0.0b

Counts

32 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
3.3b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
8.0b	(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))

series164.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma 1/6 (pow x 3) x)
48.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
32.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify97.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	140	392
1	513	356
2	2912	356
3	5002	356

prune131.0ms

Filtered

58 candidates to 45 candidates (22.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	58	3	61

Merged error: 0.0b

Counts

61 → 3

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))
5.9b	(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)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (exp x) 1.0)
80.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
64.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	214	568
1	592	522
2	2736	511
3	5001	511

prune146.0ms

Filtered

71 candidates to 56 candidates (21.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	71	3	74

Merged error: 0.0b

Counts

74 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
5.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.9b	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
28×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-pow`
18×	`exp-prod`
10×	`pow1`
9×	`distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u`
3×	`fma-def`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `exp-sum` `clear-num` `sum-log` `div-inv`

Counts

4 → 101

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
8.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
78.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
51.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
48.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

simplify131.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	275	1057
1	733	943
2	3311	927
3	5001	926

prune224.0ms

Filtered

113 candidates to 82 candidates (27.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Merged error: 0.0b

Counts

116 → 4

regimes29.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 21.3b

bsearch41.0ms

Steps

Iters	Range		Point
10	-0.010589856477353462	-1.985499863706084e-13	-0.00014016872383617292

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample897.0ms

Algorithm

intervals

Results

392.0ms	2239×	body	1280	valid
179.0ms	1623×	body	640	valid
104.0ms	5457×	body	80	valid
62.0ms	869×	body	320	valid
20.0ms	435×	body	160	valid