Details

sample99.0ms

Algorithm

intervals

Results

37.0ms	217×	body	10240	exit
31.0ms	107×	body	1280	valid
15.0ms	81×	body	640	valid
4.0ms	34×	body	320	valid
1.0ms	16×	body	160	valid
1.0ms	18×	body	80	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (45.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune7.0ms

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: 0.0b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite6.0ms

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`
4×	`log1p-expm1-u`
3×	`pow1` `expm1-log1p-u` `associate-/r` `associate-/l` `add-log-exp`
2×	`expm1-udef`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

3 → 51

Calls

3 calls:

1.0ms	(expm1 (+ x x))
1.0ms	(fma 1 1 (exp (+ x x)))
3.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series114.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(expm1 (+ x x))
21.0ms	(fma 1 1 (exp (+ x x)))
70.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify80.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382

prune134.0ms

Filtered

60 candidates to 49 candidates (81.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	5	62

Merged error: 0b

Counts

62 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(log1p (exp (* 2 x)))
0.0b	(exp (log1p (exp (* 2 x))))
0.0b	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-cbrt-cube`
5×	`add-exp-log` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
4×	`pow1`
3×	`exp-prod` `associate-/r` `associate-/l`
2×	`log1p-udef` `rem-exp-log` `expm1-udef`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `log1p-expm1` `div-exp` `clear-num` `div-inv`

Counts

4 → 66

Calls

4 calls:

1.0ms	(expm1 (+ x x))
1.0ms	(log1p (exp (* 2 x)))
2.0ms	(exp (log1p (exp (* 2 x))))
5.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(expm1 (+ x x))
51.0ms	(log1p (exp (* 2 x)))
79.0ms	(exp (log1p (exp (* 2 x))))
144.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	196	568
1	609	517
2	2717	505
3	5001	496

prune176.0ms

Filtered

78 candidates to 60 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0b

Counts

83 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* 2 x))
0.0b	(+ 1 (exp (* 2 x)))
0.0b	(/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x)))
0.4b	(/ 1 (/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
97×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`associate-/r*`
17×	`add-exp-log` `distribute-lft-out`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1` `log1p-expm1-u`
4×	`cbrt-undiv` `expm1-log1p-u`
3×	`fma-def`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `expm1-log1p` `pow-flip` `sum-log` `associate-/r/` `inv-pow` `expm1-udef`

Counts

4 → 153

Calls

4 calls:

1.0ms	(expm1 (* 2 x))
3.0ms	(+ 1 (exp (* 2 x)))
6.0ms	(/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x)))
8.0ms	(/ 1 (/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(expm1 (* 2 x))
10.0ms	(+ 1 (exp (* 2 x)))
55.0ms	(/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x)))
55.0ms	(/ 1 (/ (+ 1 (exp (* 2 x))) (expm1 (* 2 x))))

simplify58.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	459	1703
1	2406	1465
2	5001	1409

prune223.0ms

Filtered

165 candidates to 91 candidates (55.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	165	5	170

Merged error: 0b

Counts

170 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* 2 x))
0.4b	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
0.4b	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
0.9b	(/ 1 (/ (hypot 1 (exp x)) 1))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
141×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
96×	`add-cube-cbrt`
83×	`add-exp-log`
47×	`div-exp`
44×	`associate-l`
32×	`add-cbrt-cube`
20×	`prod-exp`
18×	`1-exp`
16×	`associate-/r*`
14×	`unswap-sqr`
13×	`cbrt-undiv` `associate-r`
11×	`div-inv`
9×	`rec-exp`
7×	`pow1`
6×	`cbrt-unprod` `associate-/l*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/` `expm1-udef`
1×	`frac-times` `expm1-log1p` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 233

Calls

4 calls:

1.0ms	(expm1 (* 2 x))
20.0ms	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
3.0ms	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
10.0ms	(/ 1 (/ (hypot 1 (exp x)) 1))

series372.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(expm1 (* 2 x))
149.0ms	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
119.0ms	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
87.0ms	(/ 1 (/ (hypot 1 (exp x)) 1))

simplify106.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	989	2583
1	4888	2209
2	5001	2209

prune418.0ms

Filtered

245 candidates to 146 candidates (59.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	246	4	250

Merged error: 0b

Counts

250 → 4

regimes16.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	17	7
2	17	7

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7412×	body	10240	exit
991.0ms	3330×	body	1280	valid
433.0ms	2410×	body	640	valid
134.0ms	1221×	body	320	valid
43.0ms	632×	body	160	valid
21.0ms	407×	body	80	valid