Details

analyze463.0ms (10.9%)

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

sample32.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
1.0ms	16×	body	80	nan

simplify131.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5577	24

prune18.0ms (0.4%)

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: 5.5b

Counts

2 → 1

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))

series117.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
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)

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5109	1424

prune266.0ms (6.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 4.8b

Counts

109 → 12

localize27.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms (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)

series90.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
22.0ms	(cbrt x)
22.0ms	(cbrt x)

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	765
1	4934	765

prune176.0ms (4.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Merged error: 4.8b

Counts

86 → 12

localize41.0ms (1%)

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)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms (0.8%)

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)

series172.0ms (4%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
25.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(cbrt x)

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5165	1465

prune259.0ms (6.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	115	12	127

Merged error: 4.8b

Counts

127 → 12

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(* (log x) (- x 0.5))
0.2b	(* (log x) (- x 0.5))
0.5b	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
18×	`sqrt-prod`
16×	`associate-r`
14×	`associate-l`
12×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
9×	`times-frac`
8×	`flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `flip--`
6×	`associate-*r/` `unswap-sqr`
5×	`pow-prod-down` `pow-prod-up`
4×	`frac-times` `sub-neg` `add-log-exp`
3×	`prod-exp` `associate-/r` `pow-sqr` `-commutative` `cbrt-unprod` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `log-pow` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `rem-square-sqrt` `flip-+` `div-inv`

Counts

4 → 136

Calls

4 calls:

17.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.0ms	(* (log x) (- x 0.5))
6.0ms	(* (log x) (- x 0.5))

series278.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (sqrt (- (* (log x) (- x 0.5)) x)) (sqrt (- (* (log x) (- x 0.5)) x)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(* (log x) (- x 0.5))
21.0ms	(* (log x) (- x 0.5))

simplify59.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5025	1854

prune390.0ms (9.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	148	12	160

Merged error: 4.8b

Counts

160 → 12

regimes507.0ms (11.9%)

Accuracy

Total 2.3b remaining (36%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	36
1	60	36

end0.0ms (0%)

sample904.0ms (21.3%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	80	valid
87.0ms	1183×	body	80	invalid
46.0ms	741×	body	80	nan

Details

analyze463.0ms (10.9%)

sample32.0ms (0.8%)

simplify131.0ms (3.1%)

prune18.0ms (0.4%)

localize21.0ms (0.5%)

rewrite39.0ms (0.9%)

series117.0ms (2.8%)

simplify43.0ms (1%)

prune266.0ms (6.3%)

localize27.0ms (0.6%)

rewrite16.0ms (0.4%)

series90.0ms (2.1%)

simplify57.0ms (1.3%)

prune176.0ms (4.1%)

localize41.0ms (1%)

rewrite32.0ms (0.8%)

series172.0ms (4%)

simplify43.0ms (1%)

prune259.0ms (6.1%)

localize21.0ms (0.5%)

rewrite45.0ms (1%)

series278.0ms (6.5%)

simplify59.0ms (1.4%)

prune390.0ms (9.2%)

regimes507.0ms (11.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample904.0ms (21.3%)

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