Details

sample118.0ms

Algorithm

intervals

Results

42.0ms	494×	body	80	valid
26.0ms	46×	body	1280	valid
10.0ms	131×	body	80	overflowed
8.0ms	24×	body	640	valid
4.0ms	16×	body	320	valid
2.0ms	10×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 21.7b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
1.7b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
14×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`div-sub` `associate-/r*` `div-inv`
2×	`exp-prod` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 105

Calls

4 calls:

3.0ms	(exp (* (+ 1.0 eps) x))
3.0ms	(exp (* (- 1.0 eps) x))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
132.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series78.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(exp (* (+ 1.0 eps) x))
5.0ms	(exp (* (- 1.0 eps) x))
12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
57.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	506	1621
1	1440	1536
2	5001	1520

prune287.0ms

Filtered

117 candidates to 85 candidates (27.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	3	119

Merged error: 0.0b

Counts

119 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

7.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify160.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	158	214
1	638	189
2	4553	189
3	5001	189

prune48.0ms

Filtered

36 candidates to 22 candidates (38.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Merged error: 0.0b

Counts

39 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
1.7b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))
2.5b	(log (- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

180×	`*-un-lft-identity`
166×	`times-frac`
128×	`add-sqr-sqrt`
48×	`distribute-lft-out--`
36×	`add-cube-cbrt`
29×	`log-prod`
26×	`difference-of-squares`
12×	`distribute-lft-out`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `div-inv`
4×	`log-div`
3×	`flip3--` `div-sub` `associate-/r*` `flip--`
2×	`exp-to-pow` `distribute-rgt-out--` `diff-log` `frac-sub` `associate-/l/` `sub-div`
1×	`cbrt-undiv` `sub-neg` `exp-prod` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `log-pow` `rem-exp-log` `associate--r-`

Counts

4 → 136

Calls

4 calls:

3.0ms	(exp (* (- 1.0 eps) x))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
132.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))
129.0ms	(log (- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(exp (* (- 1.0 eps) x))
12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
54.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))
103.0ms	(log (- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	718	2947
1	2365	2802
2	5002	2802

prune466.0ms

Filtered

148 candidates to 102 candidates (31.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	148	3	151

Merged error: 0.0b

Counts

151 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(exp (neg (* (+ 1.0 eps) x)))
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

6.0ms	(* (+ 1.0 eps) x)
3.0ms	(exp (neg (* (- 1.0 eps) x)))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
16.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ 1.0 eps) x)
6.0ms	(exp (neg (* (- 1.0 eps) x)))
6.0ms	(exp (neg (* (+ 1.0 eps) x)))
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify136.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	1177	3664
1	4380	3403
2	5001	3392

prune261.0ms

Filtered

160 candidates to 81 candidates (49.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	160	3	163

Merged error: 0.0b

Counts

163 → 3

regimes98.0ms

Accuracy

93.5% (1.0b remaining)

Error of 1.6b against oracle of 0.5b and baseline of 16.7b

bsearch105.0ms

Steps

Iters	Range		Point
10	2.0653047992902834e-16	1.0754636123633553e-05	1.0622204398663886e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	22
1	38	22

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	13403×	body	80	valid
784.0ms	1365×	body	1280	valid
350.0ms	981×	body	640	valid
284.0ms	3670×	body	80	overflowed
132.0ms	538×	body	320	valid
40.0ms	256×	body	160	valid

Details

sample118.0ms

simplify38.0ms

prune11.0ms

localize16.0ms

rewrite154.0ms

series78.0ms

simplify50.0ms

prune287.0ms

localize7.0ms

rewrite8.0ms

series7.0ms

simplify160.0ms

prune48.0ms

localize20.0ms

rewrite285.0ms

series175.0ms

simplify77.0ms

prune466.0ms

localize21.0ms

rewrite38.0ms

series65.0ms

simplify136.0ms

prune261.0ms

regimes98.0ms

bsearch105.0ms

simplify2.0ms

end0.0ms

sample3.2s

Profiling