Details

analyze967.0ms (15.9%)

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
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

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5321	37

prune14.0ms (0.2%)

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: 24.1b

Counts

2 → 2

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
23.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

25.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
10.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))

series57.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
9.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4994	2437
1	4994	2437

prune306.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Merged error: 0.0b

Counts

111 → 7

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
8.2b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
14.6b	(* (/ 1 (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))))
20.6b	(/ (+ (* 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)))

rewrite116.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

58.0ms	(* (/ 1 (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))))
28.0ms	(/ (+ (* 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)))
12.0ms	(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))

series104.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (+ (* 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	(* (/ 1 (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))))
7.0ms	(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))

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4960	7444
1	4960	7444

prune910.0ms (14.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Merged error: 0.0b

Counts

179 → 7

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

19.4b	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
19.4b	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
19.4b	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
23.4b	(/ (+ (* (* x (* (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)))) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite89.0ms (1.5%)

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` `cbrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 70

Calls

4 calls:

58.0ms	(/ (+ (* (* x (* (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)))) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
10.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
10.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
10.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))

series122.0ms (2%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ (* (* x (* (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)))) (cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
32.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
26.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
26.0ms	(cbrt (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4943	2577
1	4943	2577

prune320.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	82	7	89

Merged error: 0.0b

Counts

89 → 7

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
23.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
23.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
23.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite107.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

29.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
26.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
26.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
22.0ms	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series167.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
39.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
36.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
36.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5044	5802

prune1.0s (17.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	129	7	136

Merged error: 0.0b

Counts

136 → 7

regimes374.0ms (6.1%)

Accuracy

Total 0.7b remaining (94.4%)

Threshold costs 0.7b (94.4%)

bsearch51.0ms (0.8%)

Steps

Iters	Range		Point
8	1.6019824543041805e+50	7.736316388164654e+53	1.0135065295007165e+52
9	-6.319197262780983e+63	-5.833522397763109e+57	-1.3509035285611866e+59

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	92
1	93	92

end0.0ms (0%)

sample852.0ms (14%)

Algorithm

1×

intervals

Results

665.0ms	8000×	body	80	valid
1.0ms	7×	body	80	invalid

Details

analyze967.0ms (15.9%)

sample31.0ms (0.5%)

simplify34.0ms (0.6%)

prune14.0ms (0.2%)

localize22.0ms (0.4%)

rewrite56.0ms (0.9%)

series57.0ms (0.9%)

simplify50.0ms (0.8%)

prune306.0ms (5%)

localize31.0ms (0.5%)

rewrite116.0ms (1.9%)

series104.0ms (1.7%)

simplify97.0ms (1.6%)

prune910.0ms (14.9%)

localize29.0ms (0.5%)

rewrite89.0ms (1.5%)

series122.0ms (2%)

simplify54.0ms (0.9%)

prune320.0ms (5.2%)

localize30.0ms (0.5%)

rewrite107.0ms (1.8%)

series167.0ms (2.7%)

simplify66.0ms (1.1%)

prune1.0s (17.1%)

regimes374.0ms (6.1%)

bsearch51.0ms (0.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample852.0ms (14%)

Profiling