Details

analyze243.0ms

Algorithm: search

sample76.0ms

Algorithm

intervals

Results

32.0ms	58×	body	1280	valid
13.0ms	128×	body	80	valid
13.0ms	35×	body	640	valid
6.0ms	24×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	10×	body	80	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

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: 30.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
3.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg` `frac-sub`
80×	`frac-times`
61×	`neg-sub0` `exp-diff`
40×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
20×	`un-div-inv`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `exp-prod` `associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `times-frac` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

3.0ms	(exp (neg (* (- 1.0 eps) x)))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
19.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (neg (* (- 1.0 eps) x)))
12.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
49.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify148.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	1201	4059
1	4400	3786
2	5002	3771

prune342.0ms

Filtered

96 candidates to 180 candidates (-87.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	2	181

Merged error: 0.2b

Counts

181 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.4b	(- (+ (* 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` `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:

4.0ms	(* 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

prune81.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.2b

Counts

53 → 3

localize15.0ms

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))
1.7b	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
7.4b	(- (+ (* 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))
8.0ms	(- (+ (* 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (43.0ms)

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

prune178.0ms

Filtered

60 candidates to 105 candidates (-75.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	105	3	108

Merged error: 0.2b

Counts

108 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* 1.0 (pow x 2)) 3)
1.7b	(cbrt (pow (/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))) 3))
10.4b	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
11.3b	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

168×	`add-sqr-sqrt`
128×	`cbrt-prod`
117×	`times-frac`
88×	`difference-of-squares`
84×	`unpow-prod-down` `cube-prod`
80×	`*-un-lft-identity`
68×	`sqr-pow`
63×	`flip3-+` `flip-+`
60×	`associate-*r/`
58×	`add-cube-cbrt`
54×	`associate-/r/`
48×	`frac-add`
24×	`frac-times`
13×	`associate-/l*`
12×	`add-exp-log` `associate-*l/`
11×	`difference-cubes` `distribute-lft-out--`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `pow-exp`
3×	`pow-unpow` `prod-exp` `associate-/r*` `div-inv`
2×	`cube-mult` `pow-to-exp` `flip3--` `unpow3` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `div-exp` `clear-num` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 271

Calls

4 calls:

5.0ms	(pow (* 1.0 (pow x 2)) 3)
40.0ms	(cbrt (pow (/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))) 3))
13.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
31.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (* 1.0 (pow x 2)) 3)
20.0ms	(cbrt (pow (/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))) 3))
9.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
15.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 (pow x 2)) (+ (* 1.0 (pow x 2)) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))))

simplify161.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1759	12848
1	5001	12828

prune2.4s

Filtered

157 candidates to 283 candidates (-80.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	280	3	283
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	282	4	286

Merged error: 0.2b

Counts

286 → 4

regimes234.0ms

Accuracy

97.2% (0.4b remaining)

Error of 1.0b against oracle of 0.6b and baseline of 16.6b

bsearch177.0ms

Steps

Iters	Range		Point
10	2.408358116339161e-12	5218.676379625664	44.25258540111097

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	99
1	79	99
2	79	99

end0.0ms

analyze239.0ms

Algorithm: search

sample2.2s

Algorithm

intervals

Results

984.0ms	1729×	body	1280	valid
472.0ms	1288×	body	640	valid
338.0ms	4005×	body	80	valid
161.0ms	645×	body	320	valid
57.0ms	333×	body	160	valid
19.0ms	218×	body	80	invalid
15.0ms	172×	body	80	overflowed
7.0ms	12×	body	1280	invalid
4.0ms	11×	body	640	invalid
1.0ms	5×	body	160	invalid
0.0ms	1×	body	320	invalid

Details

analyze243.0ms

sample76.0ms

simplify37.0ms

prune7.0ms

localize18.0ms

rewrite57.0ms

series76.0ms

simplify148.0ms

prune342.0ms

localize10.0ms

rewrite14.0ms

series8.0ms

simplify34.0ms

prune81.0ms

localize15.0ms

rewrite32.0ms

series17.0ms

simplify54.0ms

prune178.0ms

localize25.0ms

rewrite106.0ms

series49.0ms

simplify161.0ms

prune2.4s

regimes234.0ms

bsearch177.0ms

simplify3.0ms

end0.0ms

analyze239.0ms

sample2.2s

Profiling