Details

analyze1.3s (1.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5008	220
0	3	3
1	3	3

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

Compiler

Compiled 38 to 30 computations (21.1% saved)

sample32.0ms (0%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify51.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5236	55

prune4.0ms (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

Error

29.7b

Counts

2 → 1

Compiler

Compiled 74 to 58 computations (21.6% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
0.1b	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)
28.7b	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

rewrite398.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

27.6b

Rules

18×	`add-sqr-sqrt_binary64_9989`
15×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
12×	`add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
10×	`pow1_binary64_10028`
9×	`associate-l_binary64_9908` `associate-r_binary64_9907`
8×	`associate-/l/_binary64_9914` `associate-*l/_binary64_9910`
7×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
4×	`prod-exp_binary64_10016` `add-log-exp_binary64_10006` `cbrt-unprod_binary64_10000` `frac-times_binary64_9977`
3×	`times-frac_binary64_9973` `flip3--_binary64_9971` `flip--_binary64_9942` `associate-/r_binary64_9911` `pow-prod-down_binary64_10038` `unswap-sqr_binary64_9935` `-commutative_binary64_9898`
2×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001` `associate-*r/_binary64_9909` `associate-/r/_binary64_9913`
1×	`frac-2neg_binary64_9978` `clear-num_binary64_9966` `div-inv_binary64_9964` `associate-/l*_binary64_9912`

Counts

4 → 91

Calls

4 calls:

51.0ms	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
16.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
12.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
7.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

Compiler

Compiled 4862 to 3465 computations (28.7% saved)

series2.0s (2.9%)

Error

0.8b

Counts

4 → 48

Calls

4 calls:

1.6s	(/.f64 (.f64 (-.f64 x 2) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x) y) x) z)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
134.0ms	(.f64 (+.f64 (.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x)
126.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x) 604816789577447/4398046511104) x)
58.0ms	(.f64 (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664) x)

Compiler

Compiled 6857 to 5485 computations (20% saved)

simplify137.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4996	5258
1	4996	5258

prune482.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Error

0.0b

Counts

140 → 8

Compiler

Compiled 7207 to 5144 computations (28.6% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.9b	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))
16.6b	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
16.8b	(.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))))
23.4b	(/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))

rewrite1.6s (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

126×	`add-sqr-sqrt_binary64_9989`
108×	`times-frac_binary64_9973`
95×	`*-un-lft-identity_binary64_9967`
69×	`add-cube-cbrt_binary64_10002`
63×	`sqrt-prod_binary64_9983`
36×	`associate-l_binary64_9908`
24×	`associate-r_binary64_9907`
20×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
13×	`difference-of-squares_binary64_9936` `distribute-lft-out--_binary64_9919`
12×	`associate-/r*_binary64_9911`
10×	`sqrt-div_binary64_9984`
9×	`unswap-sqr_binary64_9935`
8×	`associate-/r/_binary64_9913` `associate-/l*_binary64_9912`
7×	`pow1_binary64_10028`
6×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001` `flip3-+_binary64_9970` `flip-+_binary64_9941`
4×	`add-log-exp_binary64_10006` `div-inv_binary64_9964` `associate-/l/_binary64_9914` `prod-exp_binary64_10016` `cbrt-unprod_binary64_10000`
2×	`frac-2neg_binary64_9978` `clear-num_binary64_9966`
1×	`pow-prod-down_binary64_10038` `frac-times_binary64_9977` `associate-l/_binary64_9910` `associate-r/_binary64_9909` `*-commutative_binary64_9898` `div-sub_binary64_9972` `flip3--_binary64_9971` `flip--_binary64_9942` `pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`

Counts

4 → 205

Calls

4 calls:

38.0ms	(.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))))
9.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
8.0ms	(/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
3.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))

Compiler

Compiled 17214 to 12746 computations (26% saved)

series3.4s (4.8%)

Error

0.0b

Counts

4 → 68

Calls

4 calls:

1.5s	(.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))))
1.3s	(/.f64 (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
88.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))
74.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))

Compiler

Compiled 11836 to 9613 computations (18.8% saved)

simplify285.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5632	19053

prune2.0s (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	272	9	281

Error

0.0b

Counts

281 → 9

Compiler

Compiled 20608 to 15092 computations (26.8% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.9b	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))
7.9b	(sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
16.6b	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
22.6b	(/.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))) (sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))

rewrite1.0s (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64_9989`
43×	`*-un-lft-identity_binary64_9967`
36×	`times-frac_binary64_9973`
30×	`sqrt-prod_binary64_9983`
29×	`add-cube-cbrt_binary64_10002`
15×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
12×	`associate-/r*_binary64_9911`
8×	`sqrt-div_binary64_9984`
7×	`associate-/l/_binary64_9914` `difference-of-squares_binary64_9936` `distribute-lft-out--_binary64_9919`
6×	`pow1_binary64_10028` `flip3-+_binary64_9970` `flip-+_binary64_9941` `associate-/l*_binary64_9912`
5×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001`
4×	`add-log-exp_binary64_10006` `associate-/r/_binary64_9913`
2×	`prod-exp_binary64_10016` `cbrt-unprod_binary64_10000` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `div-inv_binary64_9964` `frac-times_binary64_9977` `associate-*r/_binary64_9909` `pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`
1×	`associate-*l/_binary64_9910` `div-sub_binary64_9972` `flip3--_binary64_9971` `flip--_binary64_9942`

Counts

4 → 124

Calls

4 calls:

41.0ms	(/.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))) (sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))
15.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
13.0ms	(sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))
3.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))

Compiler

Compiled 9670 to 7163 computations (25.9% saved)

series2.9s (4.2%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

2.4s	(/.f64 (.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))) (sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328)))
83.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
70.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))
67.0ms	(sqrt.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 x 6099563062176297/140737488355328) x) 1158907574534893/4398046511104) x) 172293041005667/549755813888) x) 6624073998258585/140737488355328))

Compiler

Compiled 12168 to 9906 computations (18.6% saved)

simplify190.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	10783
1	4954	10783

prune959.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	181	8	189

Error

0.0b

Counts

189 → 8

Compiler

Compiled 13066 to 9560 computations (26.8% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

7.9b	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))
16.5b	(/.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))))
16.6b	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
26.7b	(/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))))

rewrite20.8s (29.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

2328×	`times-frac_binary64_9973`
1260×	`add-sqr-sqrt_binary64_9989`
1259×	`*-un-lft-identity_binary64_9967`
945×	`add-cube-cbrt_binary64_10002`
741×	`sqrt-prod_binary64_9983`
157×	`difference-of-squares_binary64_9936` `distribute-lft-out--_binary64_9919`
129×	`associate-/r/_binary64_9913`
66×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
65×	`div-inv_binary64_9964`
56×	`sqrt-div_binary64_9984`
47×	`associate-/l*_binary64_9912`
33×	`associate-/r*_binary64_9911`
20×	`add-exp-log_binary64_10005` `add-cbrt-cube_binary64_10003`
10×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001`
5×	`pow1_binary64_10028` `associate-/l/_binary64_9914`
4×	`add-log-exp_binary64_10006`
3×	`frac-2neg_binary64_9978` `clear-num_binary64_9966` `div-sub_binary64_9972`
1×	`flip3--_binary64_9971` `flip--_binary64_9942` `pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`

Counts

4 → 1061

Calls

4 calls:

48.0ms	(/.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))))
16.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
7.0ms	(/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))))
3.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))

Compiler

Compiled 118874 to 88379 computations (25.7% saved)

series3.5s (4.9%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

1.5s	(/.f64 (/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328))))))))) (/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664)))))))))
1.3s	(/.f64 (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (.f64 x (+.f64 x 6099563062176297/140737488355328)))))))) (+.f64 z (.f64 x (+.f64 y (.f64 x (+.f64 604816789577447/4398046511104 (.f64 x (+.f64 (*.f64 x 4688685437421479/1125899906842624) 5537984448691291/70368744177664))))))))
99.0ms	(/.f64 (-.f64 x 2) (sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328)))))))))
81.0ms	(sqrt.f64 (+.f64 6624073998258585/140737488355328 (.f64 x (+.f64 172293041005667/549755813888 (.f64 x (+.f64 1158907574534893/4398046511104 (*.f64 x (+.f64 x 6099563062176297/140737488355328))))))))

Compiler

Compiled 16443 to 13311 computations (19% saved)

simplify1.6s (2.3%)

Algorithm

1×	egg-herbie

Counts

1127 → 1127

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	6075	163432

prune19.6s (27.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1127	0	1127
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1127	8	1135

Error

0.0b

Counts

1135 → 8

Compiler

Compiled 115180 to 84748 computations (26.4% saved)

regimes2.3s (3.3%)

Accuracy

Total 0.8b remaining (99.3%)

Threshold costs 0.8b (99.3%)

Compiler

Compiled 19581 to 15273 computations (22% saved)

bsearch141.0ms (0.2%)

Steps

Iters	Range		Point
11	1.4465903595282533e+35	1.5392582005786722e+58	6.795307804012348e+46
8	-3.6142788988219845e+39	-8.936985559543527e+36	-1.6281278315350795e+39

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	216	316
1	216	316

end0.0ms (0%)

sample5.2s (7.4%)

Algorithm

1×

intervals

Results

791.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 5114 to 3973 computations (22.3% saved)

Details

analyze1.3s (1.9%)

sample32.0ms (0%)

simplify51.0ms (0.1%)

prune4.0ms (0%)

localize38.0ms (0.1%)

rewrite398.0ms (0.6%)

series2.0s (2.9%)

simplify137.0ms (0.2%)

prune482.0ms (0.7%)

localize45.0ms (0.1%)

rewrite1.6s (2.3%)

series3.4s (4.8%)

simplify285.0ms (0.4%)

prune2.0s (2.9%)

localize40.0ms (0.1%)

rewrite1.0s (1.5%)

series2.9s (4.2%)

simplify190.0ms (0.3%)

prune959.0ms (1.4%)

localize29.0ms (0%)

rewrite20.8s (29.6%)

series3.5s (4.9%)

simplify1.6s (2.3%)

prune19.6s (27.9%)

regimes2.3s (3.3%)

bsearch141.0ms (0.2%)

simplify8.0ms (0%)

end0.0ms (0%)

sample5.2s (7.4%)

Profiling