Details

sample108.0ms

Algorithm

intervals

Results

31.0ms	77×	body	10240	exit
24.0ms	51×	body	1280	valid
19.0ms	348×	body	80	valid
13.0ms	51×	body	640	valid
3.0ms	15×	body	320	valid
0.0ms	3×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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: 28.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-log-exp`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt` `exp-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `rem-exp-log`
2×	`exp-to-pow` `associate-*l/`
1×	`neg-sub0` `distribute-lft-neg-in` `exp-neg` `neg-mul-1` `flip3--` `distribute-rgt-neg-in` `exp-diff` `diff-log` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

9.0ms	(* (- 1.0 eps) x)
3.0ms	(exp (- (* (+ 1.0 eps) x)))
3.0ms	(exp (* (- 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)))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
26.0ms	(exp (- (* (+ 1.0 eps) x)))
24.0ms	(exp (* (- 1.0 eps) x))
227.0ms	(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)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	296	507
1	952	442
2	4958	433
3	5001	433

prune271.0ms

Filtered

78 candidates to 57 candidates (73.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 6.2b

Counts

80 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 0.5 (pow x 2))
3.5b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.5b	(/ (pow x 3) eps)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
12×	`cube-prod` `associate-/l*`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqr-pow`
4×	`cube-mult` `unpow3` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `div-exp` `associate-l` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 106

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0ms	(/ (pow x 3) eps)

series96.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* 0.5 (pow x 2))
46.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms	(/ (pow x 3) eps)

simplify57.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5001	451

prune288.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 6.2b

Counts

121 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow x 3) eps)
12.8b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.8b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.8b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/l*`
9×	`add-exp-log` `cbrt-prod`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow1/3` `div-exp` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(/ (pow x 3) eps)
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (pow x 3) eps)
501.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
360.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
356.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	271	803
1	1222	747
2	5002	738

prune402.0ms

Filtered

118 candidates to 81 candidates (68.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	127	3	130

Merged error: 6.1b

Counts

130 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow x 3) eps)
4.5b	(/ (pow x 3) eps)
12.8b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
12.8b	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod` `associate-/l*`
14×	`add-exp-log`
8×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
6×	`cbrt-prod` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `div-inv`

Counts

4 → 160

Calls

4 calls:

6.0ms	(/ (pow x 3) eps)
6.0ms	(/ (pow x 3) eps)
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (pow x 3) eps)
20.0ms	(/ (pow x 3) eps)
354.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
361.0ms	(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	271	926
1	1222	878
2	5002	872

prune635.0ms

Filtered

172 candidates to 106 candidates (61.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	167	8	175

Merged error: 6.0b

Counts

175 → 8

regimes164.0ms

Accuracy

95.9% (0.7b remaining)

Error of 5.7b against oracle of 5.0b and baseline of 21.0b

bsearch154.0ms

Steps

Iters	Range		Point
9	0.08433677106829839	715934.3120435103	2.453667523275847

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	58
1	66	58
2	66	58

end0.0ms

sample3.0s

Algorithm

intervals

Results

837.0ms	1990×	body	10240	exit
781.0ms	1778×	body	1280	valid
572.0ms	9707×	body	80	valid
332.0ms	1274×	body	640	valid
111.0ms	630×	body	320	valid
42.0ms	379×	body	160	valid