Details

sample19.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	31	12
1	168	11
2	965	9
3	5001	8

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
15.1b	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`add-sqr-sqrt`
2×	`pow1` `add-cube-cbrt` `flip3--` `-un-lft-identity` `associate-l/` `associate-/r/` `flip--`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

6.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
14.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
79.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	342	496
1	1633	364
2	5001	364

prune70.0ms

Filtered

46 candidates to 29 candidates (63.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0b

Counts

47 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
0.7b	(/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))
15.2b	(* (* i i) (/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-exp-log`
57×	`prod-exp`
44×	`add-cbrt-cube`
21×	`cbrt-unprod`
18×	`div-exp`
14×	`pow1`
9×	`cbrt-undiv` `add-sqr-sqrt` `rec-exp` `1-exp` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `pow-prod-down`
5×	`add-log-exp`
4×	`associate-*l/` `associate-/r/`
3×	`flip3--` `pow-flip` `flip--` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `associate-l` `clear-num` `associate-/r` `un-div-inv` `*-commutative` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

7.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
16.0ms	(/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))
19.0ms	(* (* i i) (/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0))))

series194.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
55.0ms	(/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))
81.0ms	(* (* i i) (/ 1 (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	540	1113
1	2431	871
2	5002	859

prune115.0ms

Filtered

108 candidates to 51 candidates (47.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Merged error: 0b

Counts

112 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.00390625 (/ 1 (pow i 4))) (+ (* 0.015625 (/ 1 (pow i 2))) 0.0625))
0.2b	(/ 1 (pow i 4))
0.2b	(* 0.015625 (/ 1 (pow i 2)))
0.8b	(/ 1 (pow i 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
71×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
53×	`add-cube-cbrt`
42×	`add-exp-log`
35×	`unpow-prod-down`
28×	`associate-r`
18×	`div-exp`
15×	`associate-/r*`
13×	`add-cbrt-cube` `sqr-pow`
10×	`prod-exp`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `unpow2` `add-log-exp` `unswap-sqr`
6×	`pow1` `associate-/l*`
4×	`frac-add`
3×	`cbrt-undiv` `flip3-+` `associate-r/` `associate-l*` `sum-log` `un-div-inv` `flip-+` `div-inv`
2×	`pow-flip` `frac-2neg` `clear-num` `cbrt-unprod` `inv-pow`
1×	`+-commutative` `associate-+r+` `pow-prod-down` `*-commutative`

Counts

4 → 190

Calls

4 calls:

17.0ms	(+ (* 0.00390625 (/ 1 (pow i 4))) (+ (* 0.015625 (/ 1 (pow i 2))) 0.0625))
5.0ms	(/ 1 (pow i 4))
11.0ms	(* 0.015625 (/ 1 (pow i 2)))
5.0ms	(/ 1 (pow i 2))

series103.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* 0.00390625 (/ 1 (pow i 4))) (+ (* 0.015625 (/ 1 (pow i 2))) 0.0625))
33.0ms	(/ 1 (pow i 4))
24.0ms	(* 0.015625 (/ 1 (pow i 2)))
16.0ms	(/ 1 (pow i 2))

simplify78.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	636	1166
1	3177	953
2	5002	846

prune267.0ms

Filtered

202 candidates to 94 candidates (46.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	202	4	206

Merged error: 0b

Counts

206 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))
0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
0.5b	(log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0)))
15.3b	(/ (* i i) (* (log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (* 2.0 2.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
8×	`exp-prod`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `log-prod` `log-pow`
4×	`exp-sum`
3×	`sub-neg` `difference-of-squares`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `frac-2neg` `times-frac` `rem-log-exp` `clear-num` `associate-/r` `flip--` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

8.0ms	(exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))
7.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
7.0ms	(log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0)))
13.0ms	(/ (* i i) (* (log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (* 2.0 2.0)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))
57.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
57.0ms	(log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0)))
78.0ms	(/ (* i i) (* (log (exp (- (* (* 2.0 i) (* 2.0 i)) 1.0))) (* 2.0 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	383	770
1	1755	590
2	5001	588

prune125.0ms

Filtered

85 candidates to 54 candidates (63.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	85	4	89

Merged error: 0b

Counts

89 → 4

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.1b

bsearch20.0ms

Steps

Iters	Range		Point
4	221.35540861551883	409.0569016512947	238.72619646085138

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample437.0ms

Algorithm

intervals

Results

258.0ms	8000×	body	80	valid
83.0ms	8000×	pre	80	true