Details

sample95.0ms

Algorithm

intervals

Results

28.0ms	45×	body	1280	valid
25.0ms	337×	body	80	valid
15.0ms	45×	body	640	valid
4.0ms	57×	body	80	overflowed
4.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune9.0ms

Filtered

1 candidates to 1 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: 27.2b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
31×	`flip3--` `flip3-+` `flip--` `flip-+`
21×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
14×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out--`

Counts

4 → 182

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
19.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
48.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
31.0ms	(* (+ 1.0 eps) x)
192.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1375	4113
1	5002	3879

prune457.0ms

Filtered

194 candidates to 109 candidates (56.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	2	196

Merged error: 0.2b

Counts

196 → 2

localize9.0ms

Local error

Found 1 expressions with local error:

7.0b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify28.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	42	89
1	136	78
2	722	78
3	5002	75

prune38.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.2b

Counts

15 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

7.0b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
11.8b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.8b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
11.8b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

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 (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
150.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
148.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
146.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	190	752
1	639	693
2	2777	627
3	5001	621

prune235.0ms

Filtered

61 candidates to 58 candidates (95.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	61	3	64

Merged error: 0.2b

Counts

64 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
3.7b	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `times-frac` `associate-l/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* (- 1.0 eps) x)
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
1.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
50.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
26.0ms	(* (+ 1.0 eps) x)
234.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	462	738
1	1805	635
2	5003	628

prune254.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Merged error: 0.2b

Counts

99 → 3

regimes76.0ms

Accuracy

97.2% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch130.0ms

Steps

Iters	Range		Point
8	14.716166499582775	53889.47736569451	330.10518597305116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	21
1	46	21
2	46	21

end0.0ms

sample2.8s

Algorithm

intervals

Results

914.0ms	1699×	body	1280	valid
763.0ms	10167×	body	80	valid
424.0ms	1241×	body	640	valid
150.0ms	657×	body	320	valid
146.0ms	1978×	body	80	overflowed
47.0ms	320×	body	160	valid