Details

analyze1.0s (11.5%)

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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms

256×

body

128

valid

Compiler

Compiled 43 to 40 computations (7% saved)

simplify186.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune6.0ms (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: 17.9b

Counts

2 → 1

Compiler

Compiled 42 to 36 computations (14.3% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.6b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
17.3b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite91.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_11012`
13×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
10×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
8×	`pow1_binary64_11051`
6×	`add-log-exp_binary64_11029` `associate-r_binary64_10930` `associate-l_binary64_10931`
5×	`flip3-+_binary64_10993` `flip-+_binary64_10964`
4×	`associate-*r/_binary64_10932`
3×	`prod-exp_binary64_11039` `times-frac_binary64_10996` `associate-/r*_binary64_10934` `cbrt-unprod_binary64_11023`
2×	`associate-/l/_binary64_10937` `unswap-sqr_binary64_10958` `div-exp_binary64_11041` `associate-/r/_binary64_10936` `-commutative_binary64_10921` `cbrt-undiv_binary64_11024` `associate-l/_binary64_10933` `pow-prod-down_binary64_11061`
1×	`sum-log_binary64_11081` `clear-num_binary64_10989` `associate-/l*_binary64_10935` `+-commutative_binary64_10920` `distribute-rgt-in_binary64_10940` `frac-2neg_binary64_11001` `div-inv_binary64_10987` `distribute-lft-in_binary64_10939`

Counts

4 → 78

Calls

4 calls:

31.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
20.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
13.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
12.0ms	(+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)

series319.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
68.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
67.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
17.0ms	(+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5011	1829

prune275.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Merged error: 0b

Counts

91 → 5

Compiler

Compiled 2628 to 1948 computations (25.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)
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)))
13.6b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite104.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_11012`
22×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
19×	`times-frac_binary64_10996`
18×	`associate-r_binary64_10930`
13×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
8×	`pow1_binary64_11051`
6×	`add-log-exp_binary64_11029` `associate-l_binary64_10931`
5×	`flip3-+_binary64_10993` `flip-+_binary64_10964`
4×	`associate-/r/_binary64_10936`
3×	`prod-exp_binary64_11039` `associate-r/_binary64_10932` `unswap-sqr_binary64_10958` `associate-/l_binary64_10935` `associate-/r*_binary64_10934` `cbrt-unprod_binary64_11023`
2×	`associate-/l/_binary64_10937` `div-exp_binary64_11041` `distribute-rgt-in_binary64_10940` `div-inv_binary64_10987` `*-commutative_binary64_10921` `cbrt-undiv_binary64_11024` `associate-+l+_binary64_10923` `pow-prod-down_binary64_11061` `distribute-lft-in_binary64_10939`
1×	`sum-log_binary64_11081` `clear-num_binary64_10989` `+-commutative_binary64_10920` `frac-2neg_binary64_11001`

Counts

4 → 100

Calls

4 calls:

32.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
30.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
13.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
12.0ms	(+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)

series298.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
63.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
38.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
19.0ms	(+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)

simplify141.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4952	2860
1	4952	2860

prune305.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	113	4	117

Merged error: 0b

Counts

117 → 4

Compiler

Compiled 3455 to 2568 computations (25.7% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b	(.f64 y (log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))))
1.8b	(log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
13.6b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite136.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_11012`
33×	`add-cube-cbrt_binary64_11025` `*-un-lft-identity_binary64_10990`
32×	`log-pow_binary64_11079`
30×	`exp-prod_binary64_11042`
27×	`times-frac_binary64_10996`
22×	`associate-r_binary64_10930`
10×	`pow1_binary64_11051` `add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
9×	`log-prod_binary64_11076`
6×	`associate-/r/_binary64_10936` `associate-l_binary64_10931`
5×	`flip3-+_binary64_10993` `flip-+_binary64_10964`
4×	`add-log-exp_binary64_11029` `distribute-rgt-in_binary64_10940` `distribute-lft-in_binary64_10939`
3×	`associate-/l_binary64_10935` `associate-/r_binary64_10934` `div-inv_binary64_10987`
2×	`prod-exp_binary64_11039` `associate-/l/_binary64_10937` `associate-r/_binary64_10932` `unswap-sqr_binary64_10958` `cbrt-unprod_binary64_11023` `-commutative_binary64_10921` `pow-prod-down_binary64_11061`
1×	`rem-log-exp_binary64_11031` `clear-num_binary64_10989` `div-exp_binary64_11041` `frac-2neg_binary64_11001` `cbrt-undiv_binary64_11024`

Counts

4 → 120

Calls

4 calls:

39.0ms	(.f64 y (log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))))
31.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
28.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
13.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))

series414.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

257.0ms	(.f64 y (log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))))
66.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
52.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
39.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify139.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5067	3759

prune409.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

Compiler

Compiled 4500 to 3412 computations (24.2% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)
3.6b	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
5.0b	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
17.3b	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite137.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
16×	`add-sqr-sqrt_binary64_11012`
14×	`*-un-lft-identity_binary64_10990`
12×	`add-cube-cbrt_binary64_11025`
8×	`pow1_binary64_11051`
7×	`associate-r_binary64_10930`
6×	`times-frac_binary64_10996` `associate-r/_binary64_10932` `associate-/r_binary64_10934` `associate-l_binary64_10931`
4×	`prod-exp_binary64_11039` `associate-/l/_binary64_10937` `add-log-exp_binary64_11029` `div-exp_binary64_11041` `flip3-+_binary64_10993` `flip-+_binary64_10964` `cbrt-unprod_binary64_11023` `associate-/r/_binary64_10936` `cbrt-undiv_binary64_11024`
2×	`clear-num_binary64_10989` `unswap-sqr_binary64_10958` `associate-/l_binary64_10935` `frac-2neg_binary64_11001` `div-inv_binary64_10987` `-commutative_binary64_10921` `pow-prod-down_binary64_11061`
1×	`flip3--_binary64_10994` `flip--_binary64_10965` `distribute-lft-out_binary64_10941` `distribute-rgt-in_binary64_10940` `distribute-lft-in_binary64_10939`

Counts

4 → 91

Calls

4 calls:

43.0ms	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
42.0ms	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
23.0ms	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
8.0ms	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)

series714.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(/.f64 (.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
203.0ms	(.f64 y (+.f64 (/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
157.0ms	(/.f64 (.f64 z (+.f64 (.f64 z (.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)) -19617156695733749161611159442921/81129638414606681695789005144064)) (-.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
23.0ms	(*.f64 24929520412218516726673835482441/5192296858534827628530496329220096 z)

simplify133.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5183	2709

prune321.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	103	4	107

Merged error: 0b

Counts

107 → 4

Compiler

Compiled 3700 to 2736 computations (26.1% saved)

regimes855.0ms (9.7%)

Compiler: Compiled 3606 to 3043 computations (15.6% saved)

bsearch79.0ms (0.9%)

Steps

Iters	Range		Point
7	47862.89284855703	3173158.13290267	495134.48440773255
7	-3.91907033424736e+25	-1.9812185419073376e+24	-2.001875260796471e+24

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	84	79
1	84	79

end0.0ms (0%)

sample2.5s (27.9%)

Algorithm

1×

intervals

Results

815.0ms

8000×

body

128

valid

Compiler

Compiled 844 to 701 computations (16.9% saved)

Details

analyze1.0s (11.5%)

sample41.0ms (0.5%)

simplify186.0ms (2.1%)

prune6.0ms (0.1%)

localize35.0ms (0.4%)

rewrite91.0ms (1%)

series319.0ms (3.6%)

simplify92.0ms (1.1%)

prune275.0ms (3.1%)

localize27.0ms (0.3%)

rewrite104.0ms (1.2%)

series298.0ms (3.4%)

simplify141.0ms (1.6%)

prune305.0ms (3.5%)

localize34.0ms (0.4%)

rewrite136.0ms (1.5%)

series414.0ms (4.7%)

simplify139.0ms (1.6%)

prune409.0ms (4.6%)

localize39.0ms (0.4%)

rewrite137.0ms (1.6%)

series714.0ms (8.1%)

simplify133.0ms (1.5%)

prune321.0ms (3.6%)

regimes855.0ms (9.7%)

bsearch79.0ms (0.9%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.5s (27.9%)

Profiling