Details

analyze448.0ms (11.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample33.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	51×	body	80	invalid
2.0ms	28×	body	80	nan

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5577	24

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 6.5b

Counts

2 → 1

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`associate-l`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-log-exp`
4×	`associate-*l/`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `log-pow` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
9.0ms	(- (* (- x 0.5) (log x)) x)
8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
7.0ms	(* (- x 0.5) (log x))

series89.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* (- x 0.5) (log x)) x)
23.0ms	(* (- x 0.5) (log x))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5026	1375

prune262.0ms (6.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	12	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series88.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(cbrt x)

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	765
1	4934	765

prune186.0ms (4.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	73	13	86

Merged error: 0.0b

Counts

86 → 13

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 68

Calls

4 calls:

12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))
1.0ms	(cbrt x)

series76.0ms (2%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(cbrt x)
18.0ms	(cbrt (sqrt x))
16.0ms	(cbrt (sqrt x))

simplify57.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4960	869
1	4960	869

prune195.0ms (5.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	80	13	93

Merged error: 0.0b

Counts

93 → 13

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

14.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series173.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
24.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(cbrt x)

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5165	1465

prune229.0ms (6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	118	10	128

Merged error: 0.0b

Counts

128 → 10

regimes610.0ms (16%)

Accuracy

Total 0.2b remaining (71.5%)

Threshold costs 0.2b (71.5%)

bsearch19.0ms (0.5%)

Steps

Iters	Range		Point
6	2.2388497172259463e+23	2.367860591732093e+24	2.608303081397401e+23

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	71
1	109	71

end0.0ms (0%)

sample872.0ms (22.9%)

Algorithm

1×

intervals

Results

533.0ms	8000×	body	80	valid
75.0ms	1174×	body	80	invalid
43.0ms	740×	body	80	nan

Details

analyze448.0ms (11.8%)

sample33.0ms (0.9%)

simplify102.0ms (2.7%)

prune7.0ms (0.2%)

localize17.0ms (0.4%)

rewrite39.0ms (1%)

series89.0ms (2.3%)

simplify55.0ms (1.4%)

prune262.0ms (6.9%)

localize28.0ms (0.7%)

rewrite17.0ms (0.4%)

series88.0ms (2.3%)

simplify58.0ms (1.5%)

prune186.0ms (4.9%)

localize28.0ms (0.7%)

rewrite18.0ms (0.5%)

series76.0ms (2%)

simplify57.0ms (1.5%)

prune195.0ms (5.1%)

localize22.0ms (0.6%)

rewrite32.0ms (0.9%)

series173.0ms (4.5%)

simplify43.0ms (1.1%)

prune229.0ms (6%)

regimes610.0ms (16%)

bsearch19.0ms (0.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample872.0ms (22.9%)

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