Details

analyze106.0ms (1.8%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify215.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.6b

Counts

2 → 1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 v (.f64 -6 v))
0.3b	(*.f64 PI.f64 t)
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
0.5b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
20×	`pow1_binary64_1820`
16×	`prod-exp_binary64_1808` `associate-*r/_binary64_1706` `cbrt-unprod_binary64_1792`
13×	`add-sqr-sqrt_binary64_1783`
12×	`sqrt-div_binary64_1778` `associate-l_binary64_1705`
11×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
10×	`pow-prod-down_binary64_1830`
8×	`associate-/r/_binary64_1710` `frac-times_binary64_1772`
7×	`flip3--_binary64_1766` `flip--_binary64_1737`
6×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
5×	`associate-r_binary64_1704`
4×	`associate-*l/_binary64_1707` `cbrt-undiv_binary64_1793` `add-log-exp_binary64_1798` `div-exp_binary64_1810` `distribute-rgt-in_binary64_1714` `sub-neg_binary64_1755` `distribute-lft-in_binary64_1713`
3×	`times-frac_binary64_1768` `sqrt-prod_binary64_1777` `-commutative_binary64_1695` `associate-/l_binary64_1709`
2×	`associate-/l/_binary64_1711`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759` `unswap-sqr_binary64_1730`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
14.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
8.0ms	(.f64 v (.f64 -6 v))
4.0ms	(*.f64 PI.f64 t)

series661.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

336.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
262.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
37.0ms	(.f64 v (.f64 -6 v))
26.0ms	(*.f64 PI.f64 t)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	3576
1	4959	3576

prune213.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.2b

Counts

121 → 6

Compiler

Compiled 4348 to 2710 computations (37.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 v (.f64 v -6))
0.3b	(*.f64 PI.f64 t)
0.6b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1768`
50×	`add-sqr-sqrt_binary64_1783`
48×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
30×	`sqrt-prod_binary64_1777`
27×	`associate-/l*_binary64_1709`
11×	`pow1_binary64_1820`
10×	`prod-exp_binary64_1808` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792`
8×	`associate-/r/_binary64_1710`
7×	`associate-/r*_binary64_1708`
6×	`sqrt-div_binary64_1778` `associate-l_binary64_1705`
4×	`pow-prod-down_binary64_1830` `div-inv_binary64_1759` `add-log-exp_binary64_1798` `associate-r_binary64_1704`
3×	`div-sub_binary64_1767` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `associate-r/_binary64_1706` `flip--_binary64_1737` `-commutative_binary64_1695`
1×	`unswap-sqr_binary64_1730`

Counts

4 → 155

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
8.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
5.0ms	(.f64 v (.f64 v -6))
4.0ms	(*.f64 PI.f64 t)

series514.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

312.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
136.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
37.0ms	(.f64 v (.f64 v -6))
29.0ms	(*.f64 PI.f64 t)

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4931	6101
1	4931	6101

prune338.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	167	6	173

Merged error: 0.2b

Counts

173 → 6

Compiler

Compiled 6449 to 4119 computations (36.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 t (.f64 PI.f64 (*.f64 v v))) (sqrt.f64 2))
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 t (.f64 PI.f64 (.f64 v v))) (sqrt.f64 2))) (.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2)))))))
6.7b	(.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2))))
6.7b	(.f64 t (.f64 PI.f64 (*.f64 v v)))

rewrite73.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
31×	`pow1_binary64_1820`
25×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
19×	`pow-prod-down_binary64_1830`
18×	`add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
15×	`times-frac_binary64_1768`
9×	`associate-/r*_binary64_1708`
6×	`sqrt-prod_binary64_1777` `associate-l_binary64_1705`
5×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
4×	`add-log-exp_binary64_1798` `associate-/l*_binary64_1709`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `frac-2neg_binary64_1773` `associate-/l/_binary64_1711` `clear-num_binary64_1761` `div-inv_binary64_1759` `flip--_binary64_1737` `-commutative_binary64_1695` `associate-r*_binary64_1704`
1×	`div-sub_binary64_1767`

Counts

4 → 111

Calls

4 calls:

20.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 t (.f64 PI.f64 (.f64 v v))) (sqrt.f64 2))) (.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2)))))))
12.0ms	(.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2))))
11.0ms	(/.f64 (.f64 t (.f64 PI.f64 (*.f64 v v))) (sqrt.f64 2))
9.0ms	(.f64 t (.f64 PI.f64 (*.f64 v v)))

series911.0ms (15.8%)

Counts

4 → 12

Calls

4 calls:

645.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 t (.f64 PI.f64 (.f64 v v))) (sqrt.f64 2))) (.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2)))))))
122.0ms	(/.f64 (.f64 t (.f64 PI.f64 (*.f64 v v))) (sqrt.f64 2))
90.0ms	(.f64 t (.f64 (.f64 v v) (.f64 PI.f64 (sqrt.f64 2))))
54.0ms	(.f64 t (.f64 PI.f64 (*.f64 v v)))

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4945	4136
1	4945	4136

prune246.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Merged error: 0.2b

Counts

129 → 6

Compiler

Compiled 5853 to 3292 computations (43.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 t)
0.4b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
0.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
1.0b	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite70.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64_1797`
52×	`add-sqr-sqrt_binary64_1783`
49×	`add-cbrt-cube_binary64_1795`
46×	`times-frac_binary64_1768`
40×	`*-un-lft-identity_binary64_1762`
38×	`add-cube-cbrt_binary64_1794`
32×	`prod-exp_binary64_1808`
27×	`associate-l_binary64_1705`
25×	`div-exp_binary64_1810`
23×	`sqrt-prod_binary64_1777`
18×	`cbrt-unprod_binary64_1792`
14×	`cbrt-undiv_binary64_1793`
12×	`associate-r_binary64_1704`
10×	`pow1_binary64_1820`
8×	`associate-/r/_binary64_1710`
7×	`associate-/r*_binary64_1708`
6×	`unswap-sqr_binary64_1730` `associate-/l*_binary64_1709`
5×	`associate-*r/_binary64_1706` `1-exp_binary64_1803` `rec-exp_binary64_1809`
4×	`div-inv_binary64_1759` `add-log-exp_binary64_1798` `sqrt-div_binary64_1778`
3×	`flip3--_binary64_1766` `pow-flip_binary64_1833` `flip--_binary64_1737`
2×	`frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `*-commutative_binary64_1695`
1×	`frac-times_binary64_1772` `div-sub_binary64_1767` `inv-pow_binary64_1844` `associate-*l/_binary64_1707` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 167

Calls

4 calls:

23.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
11.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
4.0ms	(*.f64 PI.f64 t)

series562.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
132.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
83.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
28.0ms	(*.f64 PI.f64 t)

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4932	5762
1	4932	5762

prune336.0ms (5.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	179	6	185

Merged error: 0.2b

Counts

185 → 6

Compiler

Compiled 6467 to 4146 computations (35.9% saved)

regimes71.0ms (1.2%)

Compiler: Compiled 832 to 634 computations (23.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	40
1	62	40

end0.0ms (0%)

sample857.0ms (14.8%)

Algorithm

1×

intervals

Results

518.0ms	8000×	body	128	valid
1.0ms	13×	body	128	nan

Compiler

Compiled 259 to 197 computations (23.9% saved)

Details

analyze106.0ms (1.8%)

sample24.0ms (0.4%)

simplify215.0ms (3.7%)

prune4.0ms (0.1%)

localize15.0ms (0.3%)

rewrite57.0ms (1%)

series661.0ms (11.4%)

simplify85.0ms (1.5%)

prune213.0ms (3.7%)

localize17.0ms (0.3%)

rewrite56.0ms (1%)

series514.0ms (8.9%)

simplify101.0ms (1.7%)

prune338.0ms (5.8%)

localize19.0ms (0.3%)

rewrite73.0ms (1.3%)

series911.0ms (15.8%)

simplify107.0ms (1.9%)

prune246.0ms (4.2%)

localize16.0ms (0.3%)

rewrite70.0ms (1.2%)

series562.0ms (9.7%)

simplify104.0ms (1.8%)

prune336.0ms (5.8%)

regimes71.0ms (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample857.0ms (14.8%)

Profiling