Details

sample106.0ms

Algorithm

intervals

Results

29.0ms	63×	body	10240	exit
27.0ms	60×	body	1280	valid
17.0ms	304×	body	80	valid
9.0ms	32×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	15×	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: 29.9b

Counts

2 → 2

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)
5.6b	(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)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
48×	`times-frac`
36×	`add-cube-cbrt`
24×	`associate-l`
21×	`associate-r`
15×	`add-exp-log`
14×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r*`
8×	`pow1`
7×	`*-commutative` `unswap-sqr`
4×	`expm1-log1p-u` `associate-l/` `prod-exp` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`div-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3-+` `pow-prod-down` `flip-+` `associate-/l/`
1×	`flip3--` `frac-2neg` `clear-num` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

6.0ms	(* (+ 1.0 eps) x)
23.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
9.0ms	(* (- 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)))))

series359.0ms

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))))
31.0ms	(* (- 1.0 eps) x)
250.0ms	(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)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	617	1479
1	2520	1370
2	5001	1366

prune423.0ms

Filtered

152 candidates to 106 candidates (69.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	8	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Merged error: 5.0b

Counts

154 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
2.0b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0b	(/ (pow x 3) eps)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
8×	`associate-r` `associate-/l*`
7×	`add-cbrt-cube`
6×	`sqr-pow`
5×	`pow1`
4×	`unpow3` `unswap-sqr`
3×	`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` `pow-prod-down` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 91

Calls

3 calls:

9.0ms	(* 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)

series107.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* 0.5 (pow x 2))
55.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
23.0ms	(/ (pow x 3) eps)

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	290	444
1	1230	397
2	5002	387

prune206.0ms

Filtered

100 candidates to 62 candidates (62.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 5.0b

Counts

108 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
2.0b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.9b	(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
6.0b	(/ (pow x 3) eps)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

1.0ms	(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
1.0ms	(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
6.0ms	(/ (pow x 3) eps)

series756.0ms

Counts

4 → 12

Calls

4 calls:

516.0ms	(expm1 (log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))))
51.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
161.0ms	(log1p (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
27.0ms	(/ (pow x 3) eps)

simplify39.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	279	568
1	1031	510
2	5001	508

prune242.0ms

Filtered

96 candidates to 69 candidates (71.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	102	3	105

Merged error: 1.0b

Counts

105 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log 2.0) (* 0.25 (pow x 2)))
0.0b	(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

80×	`prod-diff`
76×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`add-cube-cbrt`
32×	`associate-r`
25×	`pow1`
23×	`log-pow`
20×	`unswap-sqr`
17×	`unpow-prod-down`
14×	`associate-l`
9×	`unpow2` `sqr-pow`
5×	`add-log-exp` `difference-of-squares`
4×	`fma-neg` `*-commutative` `distribute-lft-out--`
3×	`log-prod` `associate--l+` `log1p-expm1-u`
2×	`add-exp-log` `expm1-log1p-u` `diff-log` `add-cbrt-cube`
1×	`sub-neg` `expm1-log1p` `flip3--` `flip--` `expm1-udef`

Counts

2 → 122

Calls

2 calls:

15.0ms	(- (log 2.0) (* 0.25 (pow x 2)))
1.0ms	(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

series310.0ms

Counts

2 → 6

Calls

2 calls:

246.0ms	(- (log 2.0) (* 0.25 (pow x 2)))
64.0ms	(expm1 (- (log 2.0) (* 0.25 (pow x 2))))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	524	1983
1	1604	1219
2	5001	1172

prune104.0ms

Filtered

128 candidates to 39 candidates (30.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Merged error: 1.0b

Counts

131 → 5

regimes65.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 16.3b

bsearch116.0ms

Steps

Iters	Range		Point
7	14.248642872561359	1450.1527464788446	210.29207617575594

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	28
1	53	28
2	53	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

819.0ms	1895×	body	10240	exit
811.0ms	1790×	body	1280	valid
573.0ms	9976×	body	80	valid
359.0ms	1325×	body	640	valid
112.0ms	648×	body	320	valid
36.0ms	301×	body	160	valid