Details

sample588.0ms

Algorithm

intervals

Results

35.0ms	89×	body	2560	valid
25.0ms	91×	body	1280	valid
9.0ms	232×	body	80	nan
9.0ms	42×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	6×	body	80	valid

simplify99.0ms

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	5002	7

prune2.0ms

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))
0.5b	(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)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

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

prune113.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

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: 0.5b

Counts

73 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

7.0ms	(+ (pow v 2) (pow v 4))
11.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (pow v 2) (pow v 4))
8.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify154.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	177	315
1	834	276
2	4136	273
3	5002	273

prune92.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Merged error: 0.5b

Counts

55 → 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))))

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))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
10.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
10.0ms	(sqrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
4.0ms	(* (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 (106.0ms)

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

prune181.0ms

Filtered

48 candidates to 95 candidates (-97.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	94	4	98

Merged error: 0.5b

Counts

98 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `unpow-prod-down`
6×	`pow1` `sqrt-prod`
5×	`add-exp-log`
4×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`sqrt-pow1`
1×	`acos-asin` `pow-to-exp` `pow1/2` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

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

series163.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))
47.0ms	(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
45.0ms	(cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))
68.0ms	(pow (sqrt (cbrt (acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)))) 4)

simplify108.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	159	757
1	507	636
2	2303	597
3	5001	594

prune182.0ms

Filtered

43 candidates to 69 candidates (-60.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	68	5	73

Merged error: 0.5b

Counts

73 → 5

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	6
1	13	6

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	2991×	body	2560	valid
691.0ms	2486×	body	1280	valid
301.0ms	7883×	body	80	nan
256.0ms	1258×	body	640	valid
94.0ms	639×	body	320	valid
42.0ms	405×	body	160	valid
13.0ms	221×	body	80	valid

Details

sample588.0ms

simplify99.0ms

prune2.0ms

localize7.0ms

rewrite15.0ms

series11.0ms

simplify37.0ms

prune113.0ms

localize8.0ms

rewrite20.0ms

series19.0ms

simplify154.0ms

prune92.0ms

localize11.0ms

rewrite11.0ms

series27.0ms

simplify117.0ms

prune181.0ms

localize15.0ms

rewrite8.0ms

series163.0ms

simplify108.0ms

prune182.0ms

regimes52.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling