Details

sample105.0ms

Algorithm

intervals

Results

36.0ms	57×	body	1280	valid
24.0ms	317×	body	80	valid
18.0ms	52×	body	640	valid
4.0ms	18×	body	320	valid
4.0ms	48×	body	80	overflowed
0.0ms	2×	body	160	valid

simplify36.0ms

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

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 30.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
1.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
31×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`un-div-inv`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
20.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (- 1.0 eps) x)
9.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms	(* (+ 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)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1243	3854
1	4819	3583
2	5001	3583

prune308.0ms

Filtered

88 candidates to 176 candidates (-100.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Merged error: 0.3b

Counts

177 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.2b	(- (+ (* 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` `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)))

series8.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(- (+ (* 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

prune84.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

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: 0.3b

Counts

54 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
0.1b	(* 0.6666666666666667 (pow x 3))
2.4b	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
7.2b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

8.0ms	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
6.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
4.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	346	862
1	1520	806
2	5001	799

prune176.0ms

Filtered

60 candidates to 105 candidates (-75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Merged error: 0.3b

Counts

109 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (pow x 3))
0.2b	(* 12.0 (pow x 2))
7.2b	(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
10.6b	(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
3×	`cbrt-prod`
2×	`pow-to-exp` `cbrt-div` `flip3--` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `pow1/3` `unpow3` `associate--l+` `sum-log`

Counts

4 → 85

Calls

4 calls:

6.0ms	(* 8.0 (pow x 3))
5.0ms	(* 12.0 (pow x 2))
7.0ms	(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
6.0ms	(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 8.0 (pow x 3))
3.0ms	(* 12.0 (pow x 2))
4.0ms	(- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2)))
10.0ms	(cbrt (- (+ (* 8.0 (pow x 3)) 8.0) (* 12.0 (pow x 2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	419	643
1	1690	587
2	5002	569

prune152.0ms

Filtered

62 candidates to 97 candidates (-56.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

regimes186.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch88.0ms

Steps

Iters	Range		Point
9	0.003262827880282272	131215.07867019402	144.77985428400657

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	27
1	60	27
2	60	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

896.0ms	1620×	body	1280	valid
792.0ms	10232×	body	80	valid
449.0ms	1287×	body	640	valid
149.0ms	637×	body	320	valid
144.0ms	1898×	body	80	overflowed
52.0ms	332×	body	160	valid

Details

sample105.0ms

simplify36.0ms

prune7.0ms

localize17.0ms

rewrite53.0ms

series66.0ms

simplify150.0ms

prune308.0ms

localize10.0ms

rewrite14.0ms

series8.0ms

simplify34.0ms

prune84.0ms

localize13.0ms

rewrite32.0ms

series17.0ms

simplify55.0ms

prune176.0ms

localize11.0ms

rewrite27.0ms

series21.0ms

simplify56.0ms

prune152.0ms

regimes186.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling