Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

sample42.0ms (0.8%)

Algorithm

1×

intervals

Results

33.0ms

256×

body

valid

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4938	73
1	4938	73

prune15.0ms (0.3%)

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: 30.9b

Counts

2 → 2

localize46.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b	(* 0.0424060604 (pow x 4))
0.1b	(* x (* x 0.7715471019))
13.5b	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
30.3b	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))

rewrite92.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`*-un-lft-identity`
41×	`times-frac`
40×	`add-sqr-sqrt`
38×	`distribute-lft-out`
34×	`associate-r`
30×	`add-cube-cbrt`
21×	`add-exp-log`
18×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
8×	`prod-exp`
6×	`cbrt-unprod`
5×	`associate-/r*` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `associate-/r/` `associate-/l*` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num`

Counts

4 → 133

Calls

4 calls:

38.0ms	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
36.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))
5.0ms	(* 0.0424060604 (pow x 4))
5.0ms	(* x (* x 0.7715471019))

series50.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
20.0ms	(/ (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10))))))) (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12)))))))))
4.0ms	(* 0.0424060604 (pow x 4))
3.0ms	(* x (* x 0.7715471019))

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5587	7626

prune1.9s (34.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Merged error: 0b

Counts

147 → 3

localize47.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b	(* 0.1049934947 (* x x))
0.1b	(* 0.0424060604 (pow x 4))
0.1b	(* x (* x 0.7715471019))
30.4b	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))

rewrite61.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log`
33×	`*-un-lft-identity`
30×	`associate-r`
28×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
21×	`prod-exp`
19×	`pow1`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`cbrt-unprod`
10×	`associate-l`
9×	`pow-prod-down` `distribute-lft-out`
5×	`associate-*r/`
4×	`unpow-prod-down` `div-exp` `*-commutative` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `un-div-inv` `div-inv`

Counts

4 → 112

Calls

4 calls:

38.0ms	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
5.0ms	(* 0.1049934947 (* x x))
5.0ms	(* 0.0424060604 (pow x 4))
5.0ms	(* x (* x 0.7715471019))

series33.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* x (+ 1.0 (+ (* 0.1049934947 (* x x)) (+ (* 0.0424060604 (pow x 4)) (+ (* 0.0072644182 (pow x 6)) (+ (* 0.0005064034 (pow x 8)) (* 0.0001789971 (pow x 10)))))))) (/ 1 (+ 1.0 (+ (+ (* x (* x 0.7715471019)) (* (pow x 4) 0.2909738639)) (+ (* (pow x 6) 0.0694555761) (+ (* (pow x 8) 0.0140005442) (+ (* (pow x 10) 0.0008327945) (* 0.0001789971 (* 2.0 (pow x 12))))))))))
4.0ms	(* 0.0424060604 (pow x 4))
3.0ms	(* x (* x 0.7715471019))
3.0ms	(* 0.1049934947 (* x x))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5038	4018

prune1.1s (19.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	124	3	127

Merged error: 0b

Counts

127 → 3

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
0.2b	(/ 0.15298196345929327 (pow x 5))
0.6b	(/ 0.2514179000665375 (pow x 3))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac`
55×	`*-un-lft-identity`
44×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
19×	`associate-/r*`
13×	`add-exp-log`
12×	`cube-prod`
8×	`add-log-exp` `sqr-pow`
7×	`add-cbrt-cube`
6×	`div-exp` `associate-/l*`
5×	`distribute-lft-out`
4×	`cube-mult` `unpow3` `frac-add`
3×	`pow1` `sum-log`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `associate-+r+`

Counts

3 → 129

Calls

3 calls:

35.0ms	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
5.0ms	(/ 0.2514179000665375 (pow x 3))
4.0ms	(/ 0.15298196345929327 (pow x 5))

series16.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ (/ 0.2514179000665375 (pow x 3)) (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)))
4.0ms	(/ 0.15298196345929327 (pow x 5))
4.0ms	(/ 0.2514179000665375 (pow x 3))

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5159	1498

prune293.0ms (5.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	138	3	141

Merged error: 0b

Counts

141 → 3

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
0.1b	(* (pow x 4) 0.265709700396151)
0.1b	(* x (* x 0.6665536072))
12.0b	(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
12×	`*-un-lft-identity`
11×	`pow1`
10×	`add-cube-cbrt`
8×	`associate-r`
7×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`*-commutative`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `pow-exp` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 77

Calls

4 calls:

8.0ms	(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
5.0ms	(* (pow x 4) 0.265709700396151)
5.0ms	(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))
5.0ms	(* x (* x 0.6665536072))

series22.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))
6.0ms	(* x (+ 1.0 (- (* (pow x 4) 0.265709700396151) (* x (* x 0.6665536072)))))
4.0ms	(* (pow x 4) 0.265709700396151)
3.0ms	(* x (* x 0.6665536072))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4944	942
1	4944	942

prune157.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	89	3	92

Merged error: 0b

Counts

92 → 3

regimes47.0ms (0.9%)

Accuracy

Total 0.0b remaining (65.6%)

Threshold costs 0.0b (65.6%)

bsearch70.0ms (1.3%)

Steps

Iters	Range		Point
9	0.006277777667856217	1682886.7166918893	756.1667267563336
10	-1.9941737845059043e+31	-6.5355947410292e+19	-7.312697197229387e+22

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	99
1	102	99

end0.0ms (0%)

sample1.0s (18.9%)

Algorithm

1×

intervals

Results

928.0ms

8000×

body

valid

Details

analyze8.0ms (0.1%)

sample42.0ms (0.8%)

simplify82.0ms (1.5%)

prune15.0ms (0.3%)

localize46.0ms (0.9%)

rewrite92.0ms (1.7%)

series50.0ms (0.9%)

simplify95.0ms (1.8%)

prune1.9s (34.9%)

localize47.0ms (0.9%)

rewrite61.0ms (1.1%)

series33.0ms (0.6%)

simplify63.0ms (1.2%)

prune1.1s (19.7%)

localize13.0ms (0.2%)

rewrite49.0ms (0.9%)

series16.0ms (0.3%)

simplify34.0ms (0.6%)

prune293.0ms (5.4%)

localize10.0ms (0.2%)

rewrite24.0ms (0.4%)

series22.0ms (0.4%)

simplify64.0ms (1.2%)

prune157.0ms (2.9%)

regimes47.0ms (0.9%)

bsearch70.0ms (1.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (18.9%)

Profiling