Details

sample95.0ms

Algorithm

intervals

Results

41.0ms	104×	body	2560	valid
21.0ms	75×	body	1280	valid
9.0ms	265×	body	80	nan
9.0ms	45×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	7×	body	80	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite21.0ms

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:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
4.0ms	(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

prune134.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.4b

Counts

73 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.4b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite15.0ms

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:

14.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series98.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify142.0ms

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

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.4b

Counts

40 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(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))))

rewrite11.0ms

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)))
6.0ms	(* (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)))
18.0ms	(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))))

simplify117.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (107.0ms)

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	1	1	2
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Merged error: 0.4b

Counts

99 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(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)))))

rewrite24.0ms

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:

5.0ms	(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)))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
18.0ms	(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	(* (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

prune211.0ms

Filtered

117 candidates to 54 candidates (46.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	118	5	123

Merged error: 0.4b

Counts

123 → 5

regimes93.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	28
1	21	28

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	2900×	body	2560	valid
680.0ms	2543×	body	1280	valid
290.0ms	8100×	body	80	nan
249.0ms	1268×	body	640	valid
94.0ms	647×	body	320	valid
42.0ms	426×	body	160	valid
12.0ms	216×	body	80	valid

Details

sample95.0ms

simplify96.0ms

prune2.0ms

localize7.0ms

rewrite21.0ms

series112.0ms

simplify40.0ms

prune134.0ms

localize8.0ms

rewrite15.0ms

series98.0ms

simplify142.0ms

prune69.0ms

localize10.0ms

rewrite11.0ms

series51.0ms

simplify117.0ms

prune159.0ms

localize14.0ms

rewrite24.0ms

series47.0ms

simplify53.0ms

prune211.0ms

regimes93.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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