Details

analyze528.0ms (9.4%)

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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 43 to 40 computations (7% saved)

simplify166.0ms (3%)

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

Merged error: 16.7b

Counts

2 → 1

Compiler

Compiled 42 to 36 computations (14.3% saved)

localize15.0ms (0.3%)

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)
3.8b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
16.1b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_10882`
15×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
14×	`*-un-lft-identity_binary64_10861`
12×	`add-cube-cbrt_binary64_10893`
10×	`pow1_binary64_10919` `associate-l_binary64_10804`
9×	`associate-r_binary64_10803`
5×	`flip3-+_binary64_10864` `flip-+_binary64_10835`
4×	`prod-exp_binary64_10907` `associate-r/_binary64_10805` `cbrt-unprod_binary64_10891` `associate-l/_binary64_10806` `add-log-exp_binary64_10897`
3×	`pow-prod-down_binary64_10929` `-commutative_binary64_10794` `unswap-sqr_binary64_10829` `times-frac_binary64_10867` `associate-/r_binary64_10807`
2×	`associate-/r/_binary64_10809` `cbrt-undiv_binary64_10892` `div-exp_binary64_10909` `associate-/l/_binary64_10810`
1×	`associate-/l*_binary64_10808` `div-inv_binary64_10858` `frac-2neg_binary64_10872` `distribute-rgt-in_binary64_10813` `clear-num_binary64_10860` `distribute-lft-in_binary64_10812` `distribute-lft-out_binary64_10814`

Counts

4 → 88

Calls

4 calls:

22.0ms	(/.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))
8.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
7.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

series389.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
77.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
74.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
56.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5012	1847

prune167.0ms (3%)

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: 0b

Counts

101 → 5

Compiler

Compiled 2833 to 2082 computations (26.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.2b	(.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))))
12.9b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
12.9b	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
12.9b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite97.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64_10882`
66×	`times-frac_binary64_10867`
47×	`*-un-lft-identity_binary64_10861` `add-cube-cbrt_binary64_10893`
42×	`sqrt-prod_binary64_10876`
24×	`associate-r_binary64_10803` `associate-l_binary64_10804`
18×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
10×	`sqrt-div_binary64_10877`
9×	`unswap-sqr_binary64_10829`
8×	`pow1_binary64_10919`
6×	`associate-/r/_binary64_10809` `flip3-+_binary64_10864` `associate-/r*_binary64_10807` `flip-+_binary64_10835`
5×	`cbrt-undiv_binary64_10892` `div-exp_binary64_10909`
4×	`prod-exp_binary64_10907` `cbrt-unprod_binary64_10891` `add-log-exp_binary64_10897`
3×	`associate-/l*_binary64_10808` `div-inv_binary64_10858`
2×	`rem-sqrt-square_binary64_10874` `pow1/2_binary64_10938` `sqrt-pow1_binary64_10878` `associate-/l/_binary64_10810`
1×	`associate-r/_binary64_10805` `pow-prod-down_binary64_10929` `frac-times_binary64_10871` `-commutative_binary64_10794` `associate-*l/_binary64_10806` `frac-2neg_binary64_10872` `clear-num_binary64_10860`

Counts

4 → 150

Calls

4 calls:

41.0ms	(.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)))
10.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

series297.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(.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))))
63.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
35.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
32.0ms	(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5128	6204

prune397.0ms (7.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	162	5	167

Merged error: 0b

Counts

167 → 5

Compiler

Compiled 7008 to 5312 computations (24.2% saved)

localize14.0ms (0.3%)

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)))
13.4b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_10882`
26×	`*-un-lft-identity_binary64_10861`
24×	`add-cube-cbrt_binary64_10893`
22×	`associate-r_binary64_10803`
19×	`times-frac_binary64_10867`
15×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
10×	`pow1_binary64_10919`
9×	`associate-l_binary64_10804`
5×	`associate-*r/_binary64_10805` `flip3-+_binary64_10864` `flip-+_binary64_10835`
4×	`associate-/r/_binary64_10809` `prod-exp_binary64_10907` `cbrt-unprod_binary64_10891` `unswap-sqr_binary64_10829` `add-log-exp_binary64_10897`
3×	`pow-prod-down_binary64_10929` `associate-/l_binary64_10808` `-commutative_binary64_10794` `associate-/r*_binary64_10807`
2×	`cbrt-undiv_binary64_10892` `div-inv_binary64_10858` `distribute-rgt-in_binary64_10813` `div-exp_binary64_10909` `distribute-lft-in_binary64_10812` `associate-/l/_binary64_10810`
1×	`frac-2neg_binary64_10872` `clear-num_binary64_10860` `distribute-lft-out_binary64_10814`

Counts

4 → 110

Calls

4 calls:

23.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
16.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
9.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
7.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))

series349.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
71.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
51.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
42.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5180	2874

prune191.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	122	5	127

Merged error: 0b

Counts

127 → 5

Compiler

Compiled 3689 to 2724 computations (26.2% saved)

localize15.0ms (0.3%)

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))
0.3b	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
13.5b	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

rewrite73.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_10867`
64×	`add-sqr-sqrt_binary64_10882`
62×	`*-un-lft-identity_binary64_10861`
60×	`add-cube-cbrt_binary64_10893`
18×	`associate-/r*_binary64_10807`
15×	`add-exp-log_binary64_10896` `add-cbrt-cube_binary64_10894`
11×	`associate-/r/_binary64_10809`
8×	`pow1_binary64_10919` `flip3-+_binary64_10864` `flip-+_binary64_10835`
7×	`associate-r_binary64_10803`
6×	`associate-/l_binary64_10808` `div-inv_binary64_10858` `associate-l*_binary64_10804`
4×	`associate-*r/_binary64_10805` `cbrt-undiv_binary64_10892` `add-log-exp_binary64_10897` `div-exp_binary64_10909`
2×	`prod-exp_binary64_10907` `pow-prod-down_binary64_10929` `cbrt-unprod_binary64_10891` `*-commutative_binary64_10794` `unswap-sqr_binary64_10829` `frac-2neg_binary64_10872` `distribute-rgt-in_binary64_10813` `clear-num_binary64_10860` `distribute-lft-in_binary64_10812` `associate-/l/_binary64_10810`
1×	`distribute-lft-out_binary64_10814`

Counts

4 → 154

Calls

4 calls:

19.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
16.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))
8.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
7.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))

series360.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984)))
77.0ms	(.f64 z (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
57.0ms	(*.f64 z (+.f64 z 1692356830115869/281474976710656))
44.0ms	(/.f64 (+.f64 (.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248) (+.f64 (.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984))

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5020	5636

prune311.0ms (5.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	166	5	171

Merged error: 0b

Counts

171 → 5

Compiler

Compiled 5566 to 4058 computations (27.1% saved)

regimes396.0ms (7.1%)

Compiler: Compiled 3431 to 2873 computations (16.3% saved)

bsearch36.0ms (0.6%)

Steps

Iters	Range		Point
5	4.5982276829800946e-10	1.8133822721911609e-09	1.7846832667500659e-09
6	-1.2262658959034184e+80	-1.348875878166611e+79	-1.3674838296607385e+79

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	70	83
1	70	83

end0.0ms (0%)

sample1.3s (23.2%)

Algorithm

1×

intervals

Results

432.0ms

8000×

body

128

valid

Compiler

Compiled 811 to 669 computations (17.5% saved)

Details

analyze528.0ms (9.4%)

sample26.0ms (0.5%)

simplify166.0ms (3%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite57.0ms (1%)

series389.0ms (6.9%)

simplify55.0ms (1%)

prune167.0ms (3%)

localize18.0ms (0.3%)

rewrite97.0ms (1.7%)

series297.0ms (5.3%)

simplify98.0ms (1.7%)

prune397.0ms (7.1%)

localize14.0ms (0.3%)

rewrite67.0ms (1.2%)

series349.0ms (6.2%)

simplify65.0ms (1.1%)

prune191.0ms (3.4%)

localize15.0ms (0.3%)

rewrite73.0ms (1.3%)

series360.0ms (6.4%)

simplify117.0ms (2.1%)

prune311.0ms (5.5%)

regimes396.0ms (7.1%)

bsearch36.0ms (0.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (23.2%)

Profiling