Details

analyze430.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 48.311013%

Guaranteed chance to sample good point: 93.234635%

sample79.0ms

Algorithm

intervals

Results

35.0ms	58×	body	1280	valid
16.0ms	43×	body	640	valid
10.0ms	120×	body	80	valid
7.0ms	31×	body	320	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	invalid
0.0ms	3×	body	80	overflowed

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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: 32.4b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.3b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.3b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.6b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
106×	`times-frac`
90×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
10×	`distribute-lft-out` `associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*`
4×	`pow1` `div-inv` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `distribute-rgt-out--` `flip3-+` `frac-sub` `flip-+` `rem-exp-log` `sub-div` `associate--r-`

Counts

4 → 127

Calls

4 calls:

4.0ms	(exp (* (- 1.0 eps) x))
16.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
139.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series83.0ms

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)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
55.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	617	1951
1	1860	1845
2	5001	1835

prune342.0ms

Filtered

101 candidates to 139 candidates (-37.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	3	141

Merged error: 0.3b

Counts

141 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
4.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series10.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
4.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	273
1	894	245
2	5002	241

prune92.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	48	6	54

Merged error: 0.3b

Counts

54 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
8.5b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.5b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.5b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
8.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
9.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify133.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	253	983
1	904	924
2	4252	836
3	5001	836

prune342.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	64	7	71

Merged error: 0.3b

Counts

71 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.1b	(* 0.33333333333333337 (pow x 3))
7.8b	(+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
8.6b	(/ (+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`unpow-prod-down` `cube-prod` `unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
4×	`pow1` `sqr-pow`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`cube-mult` `pow-to-exp` `associate-+r+` `unpow3` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
13.0ms	(/ (+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 0.33333333333333337 (pow x 3))
4.0ms	(* 0.33333333333333337 (pow x 3))
8.0ms	(+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)))
10.0ms	(/ (+ (* (neg (* 0.5 0.5)) (pow x 4)) (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0))) (+ (* (pow x 2) (+ (* 0.33333333333333337 x) 0.5)) 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	412	1392
1	2001	1252
2	5001	1242

prune332.0ms

Filtered

81 candidates to 118 candidates (-45.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	118	7	125

Merged error: 0.3b

Counts

125 → 7

Details

analyze430.0ms

sample79.0ms

simplify37.0ms

prune11.0ms

localize17.0ms

rewrite176.0ms

series83.0ms

simplify56.0ms

prune342.0ms

localize9.0ms

rewrite14.0ms

series10.0ms

simplify35.0ms

prune92.0ms

localize13.0ms

rewrite29.0ms

series33.0ms

simplify133.0ms

prune342.0ms

localize19.0ms

rewrite33.0ms

series25.0ms

simplify67.0ms

prune332.0ms

regimes145.0ms

bsearch2.0ms

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