Details

sample98.0ms

Algorithm

intervals

Results

44.0ms	93×	body	2560	valid
24.0ms	89×	body	1280	valid
9.0ms	238×	body	80	nan
6.0ms	30×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	20×	body	160	valid
0.0ms	7×	body	80	valid

simplify105.0ms

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	5002	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: 0.7b

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))
0.7b	(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)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 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

prune145.0ms

Filtered

72 candidates to 55 candidates (76.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.6b

Counts

73 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
0.0b	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
0.2b	(* 5.0 (pow v 2))
0.7b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-sqr-sqrt`
96×	`times-frac`
81×	`*-un-lft-identity`
76×	`unpow-prod-down`
66×	`cbrt-prod`
60×	`cube-prod`
57×	`add-cube-cbrt`
48×	`difference-of-squares`
16×	`sqr-pow`
14×	`unpow2`
12×	`add-exp-log` `distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`associate-r` `associate-/r/`
5×	`pow1`
4×	`flip3--` `flip--` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `associate-l` `pow-exp` `prod-exp`
2×	`cube-div` `cube-mult` `pow-to-exp` `unpow3` `rem-cube-cbrt`
1×	`cbrt-undiv` `acos-asin` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 191

Calls

4 calls:

12.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
11.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
5.0ms	(* 5.0 (pow v 2))
1.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
136.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
32.0ms	(* 5.0 (pow v 2))
4.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

simplify99.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	823	2467
1	3262	2263
2	5003	2247

prune419.0ms

Filtered

203 candidates to 86 candidates (42.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	204	4	208

Merged error: 0.6b

Counts

208 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
2.0ms	(exp (log (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(exp (log (acos (/ (- 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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	365	766
1	1310	699
2	5002	677

prune192.0ms

Filtered

90 candidates to 65 candidates (72.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 0.6b

Counts

94 → 5

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)))
0.6b	(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:

9.0ms	(+ (pow v 2) (pow v 4))
9.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series167.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ (pow v 2) (pow v 4))
91.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
4.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify166.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (29.0ms)

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

prune90.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 0.6b

Counts

57 → 5

regimes89.0ms

Accuracy

0% (1.1b remaining)

Error of 1.6b against oracle of 0.5b and baseline of 1.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2992×	body	2560	valid
681.0ms	2501×	body	1280	valid
288.0ms	8036×	body	80	nan
249.0ms	1285×	body	640	valid
88.0ms	627×	body	320	valid
38.0ms	401×	body	160	valid
11.0ms	194×	body	80	valid

Details

sample98.0ms

simplify105.0ms

prune2.0ms

localize7.0ms

rewrite15.0ms

series115.0ms

simplify40.0ms

prune145.0ms

localize17.0ms

rewrite40.0ms

series260.0ms

simplify99.0ms

prune419.0ms

localize11.0ms

rewrite19.0ms

series112.0ms

simplify44.0ms

prune192.0ms

localize8.0ms

rewrite20.0ms

series167.0ms

simplify166.0ms

prune90.0ms

regimes89.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling