Details

sample89.0ms

Algorithm

intervals

Results

25.0ms	50×	body	1280	valid
21.0ms	310×	body	80	valid
17.0ms	44×	body	640	valid
4.0ms	67×	body	80	overflowed
3.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 27.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(exp (neg (* (+ 1.0 eps) x)))
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
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 → 155

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms	(exp (neg (* (- 1.0 eps) x)))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
26.0ms	(exp (neg (* (- 1.0 eps) x)))
30.0ms	(exp (neg (* (+ 1.0 eps) x)))
197.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1159	3849
1	4232	3585
2	5001	3574

prune378.0ms

Filtered

167 candidates to 86 candidates (51.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	3	168

Merged error: 0.2b

Counts

168 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune100.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.2b

Counts

54 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.4b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (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` `associate-+r+` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 46

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
6.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series77.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify34.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	203	264
1	840	241
2	5001	240

prune96.0ms

Filtered

52 candidates to 32 candidates (61.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Merged error: 0.2b

Counts

56 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.1b	(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
9.2b	(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
10.8b	(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
6×	`prod-exp` `add-log-exp`
4×	`pow1` `flip3-+` `cube-prod` `flip-+` `sqr-pow`
3×	`associate-/r` `associate-/l`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+r+` `distribute-lft-in` `associate-r/` `pow-exp` `associate-/r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `frac-2neg` `unpow3` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
5.0ms	(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
14.0ms	(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series274.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 0.6666666666666667 (pow x 3))
69.0ms	(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
48.0ms	(+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
117.0ms	(/ (+ (* (neg (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	568	1467
1	2800	1328
2	5001	1312

prune345.0ms

Filtered

118 candidates to 83 candidates (70.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	117	5	122

Merged error: 0.2b

Counts

122 → 5

Details

sample89.0ms

simplify37.0ms

prune6.0ms

localize20.0ms

rewrite47.0ms

series303.0ms

simplify139.0ms

prune378.0ms

localize10.0ms

rewrite15.0ms

series78.0ms

simplify34.0ms

prune100.0ms

localize10.0ms

rewrite14.0ms

series77.0ms

simplify34.0ms

prune96.0ms

localize20.0ms

rewrite37.0ms

series274.0ms

simplify96.0ms

prune345.0ms

regimes81.0ms

bsearch6.0ms

Profiling