Details

analyze517.0ms (10.8%)

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
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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 43 to 40 computations (7% saved)

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	453	31
1	453	31

prune3.0ms (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

Error

22.4b

Counts

2 → 1

Compiler

Compiled 42 to 36 computations (14.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
4.4b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
21.6b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_11694`
13×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
10×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
8×	`pow1_binary64_11733`
6×	`associate-r_binary64_11612` `add-log-exp_binary64_11711` `associate-l_binary64_11613`
5×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
4×	`associate-*r/_binary64_11614`
3×	`cbrt-unprod_binary64_11705` `associate-/r*_binary64_11616` `times-frac_binary64_11678` `prod-exp_binary64_11721`
2×	`cbrt-undiv_binary64_11706` `associate-/r/_binary64_11618` `div-exp_binary64_11723` `associate-l/_binary64_11615` `unswap-sqr_binary64_11640` `associate-/l/_binary64_11619` `-commutative_binary64_11603` `pow-prod-down_binary64_11743`
1×	`clear-num_binary64_11671` `sum-log_binary64_11763` `+-commutative_binary64_11602` `distribute-lft-in_binary64_11621` `frac-2neg_binary64_11683` `div-inv_binary64_11669` `distribute-rgt-in_binary64_11622` `associate-/l*_binary64_11617`

Counts

4 → 78

Calls

4 calls:

18.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
12.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
12.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
4.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)

series197.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
41.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
41.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
20.0ms	(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4925	1769
1	4925	1769

prune141.0ms (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

Error

Counts

91 → 5

Compiler

Compiled 2582 to 1915 computations (25.8% saved)

localize14.0ms (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)))
16.6b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite57.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_11694`
22×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
19×	`times-frac_binary64_11678`
18×	`associate-r_binary64_11612`
13×	`add-exp-log_binary64_11710` `add-cbrt-cube_binary64_11708`
8×	`pow1_binary64_11733`
6×	`add-log-exp_binary64_11711` `associate-l_binary64_11613`
5×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
4×	`associate-/r/_binary64_11618`
3×	`cbrt-unprod_binary64_11705` `associate-/r_binary64_11616` `associate-r/_binary64_11614` `unswap-sqr_binary64_11640` `prod-exp_binary64_11721` `associate-/l*_binary64_11617`
2×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723` `associate-+l+_binary64_11605` `distribute-lft-in_binary64_11621` `div-inv_binary64_11669` `associate-/l/_binary64_11619` `distribute-rgt-in_binary64_11622` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743`
1×	`clear-num_binary64_11671` `sum-log_binary64_11763` `+-commutative_binary64_11602` `frac-2neg_binary64_11683`

Counts

4 → 100

Calls

4 calls:

18.0ms	(.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))
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
7.0ms	(+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)

series168.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
36.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
27.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
10.0ms	(+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4952	2860
1	4952	2860

prune168.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Error

Counts

117 → 5

Compiler

Compiled 3489 to 2597 computations (25.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

14.4b	(.f64 (/.f64 y (.f64 (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
16.4b	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.4b	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
16.4b	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite87.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_11694`
28×	`times-frac_binary64_11678`
25×	`add-exp-log_binary64_11710`
24×	`associate-r_binary64_11612`
22×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
20×	`cbrt-div_binary64_11704` `cbrt-prod_binary64_11703`
18×	`add-cbrt-cube_binary64_11708`
15×	`associate-l_binary64_11613`
10×	`associate-/r/_binary64_11618` `flip-+_binary64_11646` `flip3-+_binary64_11675`
8×	`cbrt-unprod_binary64_11705` `prod-exp_binary64_11721`
7×	`cbrt-undiv_binary64_11706` `div-exp_binary64_11723`
6×	`pow1_binary64_11733` `unswap-sqr_binary64_11640`
5×	`frac-times_binary64_11682`
4×	`add-log-exp_binary64_11711`
3×	`associate-l/_binary64_11615` `associate-r/_binary64_11614` `pow1/3_binary64_11754`
2×	`div-inv_binary64_11669`
1×	`*-commutative_binary64_11603` `pow-prod-down_binary64_11743`

Counts

4 → 108

Calls

4 calls:

48.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
7.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
6.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series192.0ms (4%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)) (cbrt.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))) (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
30.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
29.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
27.0ms	(cbrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4947	4777
1	4947	4777

prune339.0ms (7.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Error

Counts

125 → 5

Compiler

Compiled 5957 to 4552 computations (23.6% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.2b	(/.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))))
4.4b	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
21.6b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))

rewrite71.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_11678`
34×	`add-exp-log_binary64_11710`
32×	`add-sqr-sqrt_binary64_11694`
28×	`add-cube-cbrt_binary64_11707` `*-un-lft-identity_binary64_11672`
22×	`add-cbrt-cube_binary64_11708`
14×	`div-exp_binary64_11723` `associate-*r/_binary64_11614`
11×	`associate-/r/_binary64_11618`
10×	`associate-/r*_binary64_11616`
9×	`pow1_binary64_11733`
8×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
7×	`cbrt-undiv_binary64_11706`
6×	`associate-r_binary64_11612` `prod-exp_binary64_11721` `div-inv_binary64_11669` `associate-l_binary64_11613` `associate-/l*_binary64_11617`
4×	`cbrt-unprod_binary64_11705` `add-log-exp_binary64_11711`
3×	`1-exp_binary64_11716` `rec-exp_binary64_11722`
2×	`clear-num_binary64_11671` `distribute-lft-in_binary64_11621` `unswap-sqr_binary64_11640` `frac-2neg_binary64_11683` `associate-/l/_binary64_11619` `distribute-rgt-in_binary64_11622` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743`
1×	`inv-pow_binary64_11757` `pow-flip_binary64_11746`

Counts

4 → 133

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
18.0ms	(/.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))))
11.0ms	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
7.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))

series188.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.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))))
48.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (.f64 y (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
44.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
41.0ms	(.f64 y (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4952	4247
1	4952	4247

prune231.0ms (4.8%)

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

Error

Counts

150 → 5

Compiler

Compiled 4521 to 3406 computations (24.7% saved)

regimes410.0ms (8.6%)

Accuracy

Total 0.1b remaining (94.9%)

Threshold costs 0.1b (94.9%)

Compiler

Compiled 2626 to 2213 computations (15.7% saved)

bsearch47.0ms (1%)

Steps

Iters	Range		Point
8	24835.72217731127	53770429.2672321	682252.1610908853
8	-337954356.25987446	-902586.6970862471	-7576428.372346333

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms (0%)

sample1.3s (27.6%)

Algorithm

1×

intervals

Results

424.0ms

8000×

body

128

valid

Compiler

Compiled 640 to 529 computations (17.3% saved)

Details

analyze517.0ms (10.8%)

sample24.0ms (0.5%)

simplify104.0ms (2.2%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite53.0ms (1.1%)

series197.0ms (4.1%)

simplify71.0ms (1.5%)

prune141.0ms (3%)

localize14.0ms (0.3%)

rewrite57.0ms (1.2%)

series168.0ms (3.5%)

simplify82.0ms (1.7%)

prune168.0ms (3.5%)

localize18.0ms (0.4%)

rewrite87.0ms (1.8%)

series192.0ms (4%)

simplify119.0ms (2.5%)

prune339.0ms (7.1%)

localize15.0ms (0.3%)

rewrite71.0ms (1.5%)

series188.0ms (3.9%)

simplify118.0ms (2.5%)

prune231.0ms (4.8%)

regimes410.0ms (8.6%)

bsearch47.0ms (1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (27.6%)

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