Details

sample97.0ms

Algorithm

intervals

Results

47.0ms	108×	body	2560	valid
19.0ms	74×	body	1280	valid
7.0ms	222×	body	80	nan
7.0ms	37×	body	640	valid
3.0ms	24×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	8×	body	80	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Filtered

1 candidates to 0 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: 0.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

7.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series111.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune130.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	2	73

Merged error: 0.5b

Counts

73 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.5b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

15.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series96.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify143.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	159	240
1	762	209
2	3891	208
3	5001	208

prune69.0ms

Filtered

37 candidates to 24 candidates (64.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Merged error: 0.5b

Counts

39 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0b	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b	(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
7.0ms	(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
23.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
19.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
5.0ms	(* (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))) (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))))

simplify121.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	123	882
1	451	782
2	2481	744
3	5001	717

prune159.0ms

Filtered

95 candidates to 48 candidates (50.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 0.5b

Counts

98 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0b	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0b	(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
63×	`add-sqr-sqrt`
24×	`associate-l` `unswap-sqr`
18×	`unpow-prod-down` `cube-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `associate-r`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`add-log-exp` `sqr-pow`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`acos-asin` `cube-mult` `pow-to-exp` `pow-plus` `unpow3` `pow-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
1.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
1.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
12.0ms	(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
19.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
19.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
10.0ms	(* (pow (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 3) (sqrt (sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	187	1710
1	832	1369
2	5001	1319

prune206.0ms

Filtered

117 candidates to 54 candidates (46.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	116	7	123

Merged error: 0.5b

Counts

123 → 7

regimes123.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2995×	body	2560	valid
580.0ms	2515×	body	1280	valid
228.0ms	8052×	body	80	nan
214.0ms	1265×	body	640	valid
73.0ms	615×	body	320	valid
33.0ms	392×	body	160	valid
11.0ms	218×	body	80	valid

Details

sample97.0ms

simplify98.0ms

prune2.0ms

localize7.0ms

rewrite15.0ms

series111.0ms

simplify40.0ms

prune130.0ms

localize8.0ms

rewrite16.0ms

series96.0ms

simplify143.0ms

prune69.0ms

localize11.0ms

rewrite12.0ms

series51.0ms

simplify121.0ms

prune159.0ms

localize14.0ms

rewrite19.0ms

series52.0ms

simplify53.0ms

prune206.0ms

regimes123.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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