Details

analyze869.0ms (17.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

sample94.0ms (1.8%)

Algorithm

1×

intervals

Results

41.0ms	92×	body	2560	valid
30.0ms	88×	body	1280	valid
9.0ms	41×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	2×	body	80	valid

simplify126.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5797	14

prune5.0ms (0.1%)

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: 0.4b

Counts

2 → 1

localize8.0ms (0.2%)

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)))

rewrite16.0ms (0.3%)

Algorithm

1×	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))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series13.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
3.0ms	(* 5.0 (* v v))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4960	1050
1	4960	1050

prune142.0ms (2.8%)

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

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
0.2b	(* 5.0 (* v v))
0.4b	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`associate-r`
17×	`add-exp-log`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `add-cbrt-cube`
10×	`pow1`
7×	`prod-exp`
6×	`associate-l`
5×	`cbrt-unprod`
4×	`pow-prod-down` `unswap-sqr`
3×	`flip3--` `flip--` `add-log-exp` `difference-of-squares`
2×	`frac-times` `div-exp` `associate-l/` `associate-/r/` `-commutative`
1×	`cbrt-undiv` `acos-asin` `rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv`

Counts

3 → 72

Calls

3 calls:

14.0ms	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
5.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))

series12.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0)))
3.0ms	(acos (* (- 1.0 (* 5.0 (* v v))) (/ 1 (- (* v v) 1.0))))
3.0ms	(* 5.0 (* v v))

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5224	1067

prune154.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Merged error: 0.4b

Counts

84 → 3

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* v (* (+ v (pow v 3)) 4.0))
0.4b	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

9.0ms	(* v (* (+ v (pow v 3)) 4.0))
1.0ms	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

series16.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

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

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5085	382

prune72.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	35	2	37

Merged error: 0.4b

Counts

37 → 2

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0b	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0b	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0b	(* (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))) (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))) (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))
1.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))

series211.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))) (cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))
49.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
49.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
47.0ms	(cbrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5155	1420

prune358.0ms (7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	84	3	87

Merged error: 0.4b

Counts

87 → 3

regimes77.0ms (1.5%)

Accuracy

Total 0.0b remaining (4.4%)

Threshold costs 0.0b (4.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	16
1	55	16

end0.0ms (0%)

sample2.6s (51.4%)

Algorithm

1×

intervals

Results

1.3s	3044×	body	2560	valid
723.0ms	2483×	body	1280	valid
265.0ms	1245×	body	640	valid
102.0ms	639×	body	320	valid
42.0ms	393×	body	160	valid
12.0ms	196×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze869.0ms (17.1%)

sample94.0ms (1.8%)

simplify126.0ms (2.5%)

prune5.0ms (0.1%)

localize8.0ms (0.2%)

rewrite16.0ms (0.3%)

series13.0ms (0.3%)

simplify75.0ms (1.5%)

prune142.0ms (2.8%)

localize10.0ms (0.2%)

rewrite23.0ms (0.5%)

series12.0ms (0.2%)

simplify61.0ms (1.2%)

prune154.0ms (3%)

localize9.0ms (0.2%)

rewrite11.0ms (0.2%)

series16.0ms (0.3%)

simplify37.0ms (0.7%)

prune72.0ms (1.4%)

localize14.0ms (0.3%)

rewrite11.0ms (0.2%)

series211.0ms (4.1%)

simplify44.0ms (0.9%)

prune358.0ms (7%)

regimes77.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (51.4%)

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