Details

analyze1.1s (21%)

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

sample87.0ms (1.7%)

Algorithm

1×

intervals

Results

42.0ms	92×	body	2560	valid
22.0ms	73×	body	1280	valid
9.0ms	43×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	10×	body	80	valid

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

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: 0.7b

Counts

2 → 1

localize9.0ms (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))
0.7b	(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))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series12.0ms (0.2%)

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))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4960	1050
1	4960	1050

prune150.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.7b

Counts

73 → 4

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.7b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
4×	`associate-/r*`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series20.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
3.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
3.0ms	(* 5.0 (* v v))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5203	1507

prune196.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Merged error: 0.7b

Counts

94 → 5

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(* v (* (+ v (pow v 3)) 4.0))
0.7b	(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:

10.0ms	(* v (* (+ v (pow v 3)) 4.0))
1.0ms	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

series14.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(* v (* (+ v (pow v 3)) 4.0))
4.0ms	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5085	382

prune80.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	34	5	39

Merged error: 0.7b

Counts

39 → 5

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))
0.9b	(sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
0.9b	(sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0b	(* (sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))) (sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))

rewrite12.0ms (0.2%)

Algorithm

1×	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:

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

series28.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
10.0ms	(sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
5.0ms	(* (sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))) (sqrt (acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))
3.0ms	(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4907	1280
1	4907	1280

prune275.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	94	6	100

Merged error: 0.7b

Counts

100 → 6

regimes136.0ms (2.6%)

Accuracy

Total 0.0b remaining (3.2%)

Threshold costs 0.0b (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	18
1	64	18

end0.0ms (0%)

sample2.6s (50.4%)

Algorithm

1×

intervals

Results

1.3s	2986×	body	2560	valid
720.0ms	2423×	body	1280	valid
279.0ms	1266×	body	640	valid
105.0ms	644×	body	320	valid
53.0ms	464×	body	160	valid
13.0ms	217×	body	80	valid
0.0ms	12×	body	80	nan

Details

analyze1.1s (21%)

sample87.0ms (1.7%)

simplify108.0ms (2.1%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite16.0ms (0.3%)

series12.0ms (0.2%)

simplify80.0ms (1.5%)

prune150.0ms (2.9%)

localize12.0ms (0.2%)

rewrite25.0ms (0.5%)

series20.0ms (0.4%)

simplify70.0ms (1.3%)

prune196.0ms (3.8%)

localize9.0ms (0.2%)

rewrite11.0ms (0.2%)

series14.0ms (0.3%)

simplify36.0ms (0.7%)

prune80.0ms (1.5%)

localize12.0ms (0.2%)

rewrite12.0ms (0.2%)

series28.0ms (0.5%)

simplify77.0ms (1.5%)

prune275.0ms (5.3%)

regimes136.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (50.4%)

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