Details

analyze967.0ms (12.8%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

valid

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5321	37

prune11.0ms (0.1%)

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: 24.5b

Counts

2 → 1

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
23.6b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `times-frac` `pow-prod-down` `associate-/r` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

30.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
10.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)

series58.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
9.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
6.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
4.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5346	2217

prune539.0ms (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
14.3b	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
14.5b	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
19.8b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite124.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

60.0ms	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
16.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
11.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series107.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
40.0ms	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))
8.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4954	9529
1	4954	9529

prune1.5s (20.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	217	9	226

Merged error: 0.0b

Counts

226 → 9

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
6.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
14.3b	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
19.6b	(/ (* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite91.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
36×	`times-frac`
30×	`sqrt-prod`
29×	`add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`sqrt-div`
7×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `flip3-+` `flip-+` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`associate-/r/` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`flip3--` `div-sub` `associate-*l/` `flip--`

Counts

4 → 124

Calls

4 calls:

48.0ms	(/ (* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
11.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series65.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z)) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
8.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
6.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5726	4487

prune589.0ms (7.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	136	9	145

Merged error: 0.0b

Counts

145 → 9

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

12.3b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.3b	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
14.3b	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
14.5b	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))))

rewrite99.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log`
68×	`add-sqr-sqrt` `*-un-lft-identity`
60×	`times-frac`
47×	`add-cbrt-cube`
42×	`add-cube-cbrt`
36×	`associate-l`
34×	`prod-exp`
33×	`sqrt-prod`
26×	`div-exp`
18×	`cbrt-unprod`
14×	`cbrt-undiv`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1`
6×	`cbrt-prod` `associate-/r*`
5×	`frac-times` `associate-r/` `associate-/l`
4×	`rec-exp` `cbrt-div` `flip3-+` `sqrt-div` `1-exp` `associate-/r/` `flip-+` `add-log-exp`
3×	`pow-prod-down` `associate-*l/`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r` `clear-num` `*-commutative` `flip--`

Counts

4 → 166

Calls

4 calls:

53.0ms	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))))
16.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series282.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (* (/ 1 (fabs (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))) (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))))))
12.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
10.0ms	(cbrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
8.0ms	(/ (- x 2.0) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4945	9155
1	4945	9155

prune1.4s (18.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	178	9	187

Merged error: 0.0b

Counts

187 → 9

regimes346.0ms (4.6%)

Accuracy

Total 0.8b remaining (96.1%)

Threshold costs 0.8b (96.1%)

bsearch41.0ms (0.5%)

Steps

Iters	Range		Point
5	1.179567413121447e+33	3.1677973372550355e+33	3.110893828765909e+33
9	-3.348902037995943e+71	-8.392682102201323e+65	-9.42722712682916e+65

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	75
1	80	75

end0.0ms (0%)

sample826.0ms (10.9%)

Algorithm

1×

intervals

Results

650.0ms	8000×	body	80	valid
1.0ms	7×	body	80	invalid

Details

analyze967.0ms (12.8%)

sample30.0ms (0.4%)

simplify41.0ms (0.5%)

prune11.0ms (0.1%)

localize23.0ms (0.3%)

rewrite63.0ms (0.8%)

series58.0ms (0.8%)

simplify51.0ms (0.7%)

prune539.0ms (7.1%)

localize28.0ms (0.4%)

rewrite124.0ms (1.6%)

series107.0ms (1.4%)

simplify100.0ms (1.3%)

prune1.5s (20.1%)

localize33.0ms (0.4%)

rewrite91.0ms (1.2%)

series65.0ms (0.9%)

simplify45.0ms (0.6%)

prune589.0ms (7.8%)

localize32.0ms (0.4%)

rewrite99.0ms (1.3%)

series282.0ms (3.7%)

simplify84.0ms (1.1%)

prune1.4s (18.2%)

regimes346.0ms (4.6%)

bsearch41.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample826.0ms (10.9%)

Profiling