Details

analyze525.0ms

Algorithm

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

sample27.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 21.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.8b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
21.2b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_4411`
13×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
10×	`*-un-lft-identity_binary64_4426` `add-cube-cbrt_binary64_4397`
8×	`pow1_binary64_4372`
6×	`associate-r_binary64_4485` `associate-l_binary64_4486` `add-log-exp_binary64_4391`
5×	`flip-+_binary64_4451` `flip3-+_binary64_4424`
4×	`associate-*r/_binary64_4487`
3×	`associate-/r*_binary64_4489` `times-frac_binary64_4421` `prod-exp_binary64_4377` `cbrt-unprod_binary64_4395`
2×	`associate-/l/_binary64_4492` `-commutative_binary64_4494` `unswap-sqr_binary64_4454` `div-exp_binary64_4379` `cbrt-undiv_binary64_4396` `associate-l/_binary64_4488` `pow-prod-down_binary64_4353` `associate-/r/_binary64_4491`
1×	`distribute-rgt-in_binary64_4469` `associate-/l*_binary64_4490` `div-inv_binary64_4427` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `distribute-lft-in_binary64_4468` `+-commutative_binary64_4493` `sum-log_binary64_4341`

Counts

4 → 78

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
11.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
17.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series202.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
37.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
44.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
99.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify70.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4999	1769
1	4999	1769

prune566.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

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

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.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)))
17.6b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_4411`
22×	`*-un-lft-identity_binary64_4426` `add-cube-cbrt_binary64_4397`
19×	`times-frac_binary64_4421`
18×	`associate-r_binary64_4485`
13×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
8×	`pow1_binary64_4372`
6×	`associate-l_binary64_4486` `add-log-exp_binary64_4391`
5×	`flip-+_binary64_4451` `flip3-+_binary64_4424`
4×	`associate-/r/_binary64_4491`
3×	`unswap-sqr_binary64_4454` `associate-/l_binary64_4490` `associate-/r_binary64_4489` `associate-*r/_binary64_4487` `prod-exp_binary64_4377` `cbrt-unprod_binary64_4395`
2×	`associate-/l/_binary64_4492` `*-commutative_binary64_4494` `div-inv_binary64_4427` `div-exp_binary64_4379` `cbrt-undiv_binary64_4396` `pow-prod-down_binary64_4353`
1×	`distribute-rgt-in_binary64_4469` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `distribute-lft-in_binary64_4468` `+-commutative_binary64_4493` `sum-log_binary64_4341`

Counts

4 → 98

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
17.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
15.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series186.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
40.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
99.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
24.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify76.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5196	2786

prune440.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Merged error: 0b

Counts

115 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.3b	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
17.6b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64_4421`
60×	`add-sqr-sqrt_binary64_4411`
58×	`*-un-lft-identity_binary64_4426` `add-cube-cbrt_binary64_4397`
18×	`associate-/r*_binary64_4489`
13×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
11×	`associate-/r/_binary64_4491`
8×	`flip-+_binary64_4451` `flip3-+_binary64_4424`
6×	`associate-/l*_binary64_4490` `pow1_binary64_4372` `div-inv_binary64_4427` `add-log-exp_binary64_4391`
4×	`div-exp_binary64_4379` `cbrt-undiv_binary64_4396`
3×	`associate-r_binary64_4485` `associate-l_binary64_4486`
2×	`associate-/l/_binary64_4492` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `associate-*r/_binary64_4487`
1×	`distribute-rgt-in_binary64_4469` `*-commutative_binary64_4494` `unswap-sqr_binary64_4454` `pow-prod-down_binary64_4353` `distribute-lft-in_binary64_4468` `+-commutative_binary64_4493` `prod-exp_binary64_4377` `cbrt-unprod_binary64_4395` `sum-log_binary64_4341`

Counts

4 → 142

Calls

4 calls:

4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
22.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
15.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

series175.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
41.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
90.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
25.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify126.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4941	5623
1	4941	5623

prune692.0ms

Filtered

124 candidates to 154 candidates (-24.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	154	5	159

Merged error: 0b

Counts

159 → 5

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
1.0b	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
3.8b	(.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984))
21.2b	(/.f64 (.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_4411`
11×	`add-exp-log_binary64_4390` `add-cbrt-cube_binary64_4398`
10×	`*-un-lft-identity_binary64_4426` `add-cube-cbrt_binary64_4397`
6×	`pow1_binary64_4372` `cbrt-prod_binary64_4393`
5×	`flip-+_binary64_4451` `flip3-+_binary64_4424`
4×	`cbrt-div_binary64_4394` `associate-*r/_binary64_4487` `add-log-exp_binary64_4391`
3×	`associate-r_binary64_4485` `associate-/r_binary64_4489` `associate-l*_binary64_4486` `times-frac_binary64_4421`
2×	`associate-/l/_binary64_4492` `div-exp_binary64_4379` `cbrt-undiv_binary64_4396` `pow1/3_binary64_4364` `prod-exp_binary64_4377` `cbrt-unprod_binary64_4395` `associate-/r/_binary64_4491`
1×	`distribute-rgt-in_binary64_4469` `-commutative_binary64_4494` `unswap-sqr_binary64_4454` `associate-/l_binary64_4490` `div-inv_binary64_4427` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `pow-prod-down_binary64_4353` `distribute-lft-in_binary64_4468`

Counts

4 → 73

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
4.0ms	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
26.0ms	(.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984))
32.0ms	(/.f64 (.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

series214.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
34.0ms	(cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
46.0ms	(.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984))
103.0ms	(/.f64 (.f64 y (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))) (.f64 z (cbrt.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)))) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

simplify99.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4956	2360
1	4956	2360

prune390.0ms

Filtered

74 candidates to 85 candidates (-14.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	85	5	90

Merged error: 0b

Counts

90 → 5

regimes334.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.4b

bsearch67.0ms

Steps

Iters	Range	Point
9	1805486889010053/70368744177664	8746386028947969/524288	622271.4209002672
10	-64257037277762263907099722673238044840017633031588264925450959658285175336713979871027625619450689587765709098483890807553553934935328012418525430473663522563245050771275776	-10109535792799053768866341326212111833988429462460899537676797128770010660105589343165299940488668524548026384871493647023146257969590539730772457596911616	-1.3770691381251735e+154

Iters

Range

Point

1805486889010053/70368744177664

8746386028947969/524288

622271.4209002672

-64257037277762263907099722673238044840017633031588264925450959658285175336713979871027625619450689587765709098483890807553553934935328012418525430473663522563245050771275776

-10109535792799053768866341326212111833988429462460899537676797128770010660105589343165299940488668524548026384871493647023146257969590539730772457596911616

-1.3770691381251735e+154

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms

sample664.0ms

Algorithm

intervals

Results

431.0ms

8000×

body

valid

Details

analyze525.0ms

sample27.0ms

simplify31.0ms

prune12.0ms

localize22.0ms

rewrite40.0ms

series202.0ms

simplify70.0ms

prune566.0ms

localize29.0ms

rewrite46.0ms

series186.0ms

simplify76.0ms

prune440.0ms

localize23.0ms

rewrite54.0ms

series175.0ms

simplify126.0ms

prune692.0ms

localize34.0ms

rewrite68.0ms

series214.0ms

simplify99.0ms

prune390.0ms

regimes334.0ms

bsearch67.0ms

simplify5.0ms

end0.0ms

sample664.0ms

Profiling