Details

analyze735.0ms (9.5%)

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%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 22 to 19 computations (13.6% saved)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

26.0ms

256×

body

128

valid

Compiler

Compiled 43 to 40 computations (7% saved)

simplify277.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune3.0ms (0%)

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: 20.0b

Counts

2 → 1

Compiler

Compiled 42 to 36 computations (14.3% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.1b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
19.5b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite87.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_12035`
15×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
14×	`*-un-lft-identity_binary64_12013`
12×	`add-cube-cbrt_binary64_12048`
10×	`associate-l_binary64_11954` `pow1_binary64_12074`
9×	`associate-r_binary64_11953`
5×	`flip3-+_binary64_12016` `flip-+_binary64_11987`
4×	`add-log-exp_binary64_12052` `associate-l/_binary64_11956` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `associate-r/_binary64_11955`
3×	`times-frac_binary64_12019` `-commutative_binary64_11944` `associate-/r_binary64_11957` `unswap-sqr_binary64_11981` `pow-prod-down_binary64_12084`
2×	`associate-/r/_binary64_11959` `div-exp_binary64_12064` `cbrt-undiv_binary64_12047` `associate-/l/_binary64_11960`
1×	`distribute-lft-out_binary64_11964` `distribute-lft-in_binary64_11962` `clear-num_binary64_12012` `div-inv_binary64_12010` `frac-2neg_binary64_12024` `associate-/l*_binary64_11958` `distribute-rgt-in_binary64_11963`

Counts

4 → 88

Calls

4 calls:

33.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
22.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
15.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
8.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

series640.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

292.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
148.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
126.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
74.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5057	1847

prune220.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

Compiler

Compiled 2848 to 2097 computations (26.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
15.4b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite81.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_12035`
26×	`*-un-lft-identity_binary64_12013`
24×	`add-cube-cbrt_binary64_12048`
22×	`associate-r_binary64_11953`
19×	`times-frac_binary64_12019`
15×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
10×	`pow1_binary64_12074`
9×	`associate-l_binary64_11954`
5×	`flip3-+_binary64_12016` `flip-+_binary64_11987` `associate-*r/_binary64_11955`
4×	`associate-/r/_binary64_11959` `add-log-exp_binary64_12052` `unswap-sqr_binary64_11981` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
3×	`-commutative_binary64_11944` `associate-/r_binary64_11957` `pow-prod-down_binary64_12084` `associate-/l*_binary64_11958`
2×	`distribute-lft-in_binary64_11962` `div-exp_binary64_12064` `div-inv_binary64_12010` `cbrt-undiv_binary64_12047` `distribute-rgt-in_binary64_11963` `associate-/l/_binary64_11960`
1×	`distribute-lft-out_binary64_11964` `clear-num_binary64_12012` `frac-2neg_binary64_12024`

Counts

4 → 110

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
26.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
8.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
7.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))

series465.0ms (6%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
111.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
61.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
55.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5206	2874

prune244.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	122	5	127

Merged error: 0.0b

Counts

127 → 5

Compiler

Compiled 3735 to 2765 computations (26% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
14.6b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
14.7b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
14.7b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite132.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64_12035`
66×	`times-frac_binary64_12019`
47×	`add-cube-cbrt_binary64_12048` `*-un-lft-identity_binary64_12013`
42×	`sqrt-prod_binary64_12029`
24×	`associate-l_binary64_11954` `associate-r_binary64_11953`
18×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
10×	`sqrt-div_binary64_12030`
9×	`unswap-sqr_binary64_11981`
8×	`pow1_binary64_12074`
6×	`associate-/r/_binary64_11959` `flip3-+_binary64_12016` `associate-/r*_binary64_11957` `flip-+_binary64_11987`
5×	`div-exp_binary64_12064` `cbrt-undiv_binary64_12047`
4×	`add-log-exp_binary64_12052` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`
3×	`div-inv_binary64_12010` `associate-/l*_binary64_11958`
2×	`pow1/2_binary64_12093` `rem-sqrt-square_binary64_12026` `sqrt-pow1_binary64_12031` `associate-/l/_binary64_11960`
1×	`-commutative_binary64_11944` `clear-num_binary64_12012` `pow-prod-down_binary64_12084` `associate-l/_binary64_11956` `frac-2neg_binary64_12024` `associate-*r/_binary64_11955` `frac-times_binary64_12023`

Counts

4 → 150

Calls

4 calls:

57.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
18.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series430.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(.f64 (/.f64 y (sqrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
108.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
47.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
37.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify142.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5233	6204

prune633.0ms (8.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	162	5	167

Merged error: 0.0b

Counts

167 → 5

Compiler

Compiled 7002 to 5309 computations (24.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.3b	(/.f64 1 (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
3.1b	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
19.5b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))

rewrite102.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_12019`
34×	`add-exp-log_binary64_12051`
32×	`add-sqr-sqrt_binary64_12035`
28×	`add-cube-cbrt_binary64_12048` `*-un-lft-identity_binary64_12013`
22×	`add-cbrt-cube_binary64_12049`
14×	`div-exp_binary64_12064` `associate-*r/_binary64_11955`
11×	`associate-/r/_binary64_11959`
10×	`associate-/r*_binary64_11957`
9×	`pow1_binary64_12074`
8×	`flip3-+_binary64_12016` `flip-+_binary64_11987`
7×	`cbrt-undiv_binary64_12047`
6×	`associate-l_binary64_11954` `div-inv_binary64_12010` `associate-/l_binary64_11958` `prod-exp_binary64_12062` `associate-r*_binary64_11953`
4×	`add-log-exp_binary64_12052` `cbrt-unprod_binary64_12046`
3×	`rec-exp_binary64_12063` `1-exp_binary64_12057`
2×	`distribute-lft-in_binary64_11962` `*-commutative_binary64_11944` `clear-num_binary64_12012` `unswap-sqr_binary64_11981` `pow-prod-down_binary64_12084` `frac-2neg_binary64_12024` `distribute-rgt-in_binary64_11963` `associate-/l/_binary64_11960`
1×	`pow-flip_binary64_12087` `inv-pow_binary64_12098`

Counts

4 → 133

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
24.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
15.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
12.0ms	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

series407.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))))
105.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
90.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
88.0ms	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify157.0ms (2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4926	4247
1	4926	4247

prune316.0ms (4.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	145	5	150

Merged error: 0.0b

Counts

150 → 5

Compiler

Compiled 4521 to 3406 computations (24.7% saved)

regimes503.0ms (6.5%)

Compiler: Compiled 2621 to 2203 computations (15.9% saved)

bsearch99.0ms (1.3%)

Steps

Iters	Range		Point
10	0.014870874547570833	59886653362.35599	45109051.99622894
9	-1.0646880069165195e+20	-1860839716431.0972	-510847591603685.9

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms (0%)

sample1.7s (22.5%)

Algorithm

1×

intervals

Results

667.0ms

8000×

body

128

valid

Compiler

Compiled 639 to 527 computations (17.5% saved)

Details

analyze735.0ms (9.5%)

sample45.0ms (0.6%)

simplify277.0ms (3.6%)

prune3.0ms (0%)

localize31.0ms (0.4%)

rewrite87.0ms (1.1%)

series640.0ms (8.3%)

simplify78.0ms (1%)

prune220.0ms (2.8%)

localize15.0ms (0.2%)

rewrite81.0ms (1%)

series465.0ms (6%)

simplify103.0ms (1.3%)

prune244.0ms (3.2%)

localize19.0ms (0.2%)

rewrite132.0ms (1.7%)

series430.0ms (5.6%)

simplify142.0ms (1.8%)

prune633.0ms (8.2%)

localize16.0ms (0.2%)

rewrite102.0ms (1.3%)

series407.0ms (5.3%)

simplify157.0ms (2%)

prune316.0ms (4.1%)

regimes503.0ms (6.5%)

bsearch99.0ms (1.3%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.7s (22.5%)

Profiling