Details

analyze109.0ms (1.7%)

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)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify204.0ms (3.2%)

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: 0.4b

Counts

2 → 1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.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)))))
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))

rewrite57.0ms (0.9%)

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`
14×	`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` `unswap-sqr_binary64_1730`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759`

Counts

4 → 109

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))))
6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series641.0ms (10%)

Counts

4 → 12

Calls

4 calls:

321.0ms	(/.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)))))
257.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
37.0ms	(.f64 5 (.f64 v v))
26.0ms	(*.f64 PI.f64 t)

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4976	3590
1	4976	3590

prune227.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.0b

Counts

122 → 7

Compiler

Compiled 4494 to 2815 computations (37.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 v v) 5)
0.2b	(*.f64 PI.f64 t)
0.4b	(/.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)))))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1768`
51×	`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-r_binary64_1704`
4×	`pow-prod-down_binary64_1830` `div-inv_binary64_1759` `add-log-exp_binary64_1798` `associate-l_binary64_1705`
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` `unswap-sqr_binary64_1730` `associate-r/_binary64_1706` `flip--_binary64_1737` `-commutative_binary64_1695`

Counts

4 → 156

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)))))
6.0ms	(.f64 (.f64 v v) 5)
4.0ms	(*.f64 PI.f64 t)

series508.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

309.0ms	(/.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))))
133.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
36.0ms	(.f64 (.f64 v v) 5)
30.0ms	(*.f64 PI.f64 t)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4937	6117
1	4937	6117

prune315.0ms (4.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	167	8	175

Merged error: 0b

Counts

175 → 8

Compiler

Compiled 6597 to 4236 computations (35.8% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (/.f64 (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (*.f64 v v))))))
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (*.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6))))

rewrite87.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64_1768`
40×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
32×	`*-un-lft-identity_binary64_1762`
31×	`add-sqr-sqrt_binary64_1783`
28×	`add-cube-cbrt_binary64_1794`
20×	`pow1_binary64_1820`
16×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
12×	`associate-l_binary64_1705`
10×	`pow-prod-down_binary64_1830` `associate-/r*_binary64_1708`
9×	`associate-/r/_binary64_1710` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
8×	`associate-*r/_binary64_1706`
7×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
6×	`sqrt-div_binary64_1778`
5×	`div-inv_binary64_1759` `associate-r_binary64_1704`
4×	`flip3--_binary64_1766` `frac-times_binary64_1772` `add-log-exp_binary64_1798` `distribute-rgt-in_binary64_1714` `flip--_binary64_1737` `sub-neg_binary64_1755` `distribute-lft-in_binary64_1713` `distribute-lft-out_binary64_1715`
3×	`sqrt-prod_binary64_1777` `-commutative_binary64_1695` `associate-/l_binary64_1709`
2×	`associate-/l/_binary64_1711` `unswap-sqr_binary64_1730` `associate-*l/_binary64_1707`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761`

Counts

4 → 140

Calls

4 calls:

36.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (/.f64 (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (*.f64 v v))))))
17.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (*.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6))))
6.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series843.0ms (13.2%)

Counts

4 → 12

Calls

4 calls:

549.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (/.f64 (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 1 (*.f64 v v))))))
231.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))) (.f64 (*.f64 PI.f64 t) (-.f64 1 (pow.f64 v 6))))
37.0ms	(.f64 5 (.f64 v v))
25.0ms	(*.f64 PI.f64 t)

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4982	6886
1	4982	6886

prune431.0ms (6.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	152	8	160

Merged error: 0b

Counts

160 → 8

Compiler

Compiled 8279 to 5168 computations (37.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 t)
0.2b	(/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v)))))
1.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))

rewrite87.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-exp-log_binary64_1797`
52×	`add-cbrt-cube_binary64_1795`
30×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
28×	`add-sqr-sqrt_binary64_1783`
26×	`times-frac_binary64_1768`
22×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
20×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
15×	`associate-l_binary64_1705` `associate-r_binary64_1704`
14×	`cbrt-div_binary64_1791`
10×	`associate-/l/_binary64_1711` `sqrt-prod_binary64_1777`
9×	`flip3--_binary64_1766` `cbrt-prod_binary64_1790` `flip--_binary64_1737`
8×	`associate-/r/_binary64_1710` `pow1_binary64_1820`
7×	`associate-/r_binary64_1708` `associate-r/_binary64_1706` `associate-/l*_binary64_1709`
5×	`frac-times_binary64_1772`
4×	`div-inv_binary64_1759` `unswap-sqr_binary64_1730` `add-log-exp_binary64_1798` `sqrt-div_binary64_1778`
3×	`associate-*l/_binary64_1707`
2×	`frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `*-commutative_binary64_1695`

Counts

4 → 151

Calls

4 calls:

29.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v)))))
17.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))
11.0ms	(/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
4.0ms	(*.f64 PI.f64 t)

series935.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
318.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v)))))
256.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (cbrt.f64 (-.f64 1 (.f64 (.f64 v v) 5)))) (sqrt.f64 (+.f64 2 (.f64 v (*.f64 v -6)))))
26.0ms	(*.f64 PI.f64 t)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4961	6879
1	4961	6879

prune445.0ms (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	165	6	171

Merged error: 0b

Counts

171 → 6

Compiler

Compiled 8320 to 5368 computations (35.5% saved)

regimes60.0ms (0.9%)

Compiler: Compiled 703 to 547 computations (22.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	40
1	62	40

end0.0ms (0%)

sample901.0ms (14.1%)

Algorithm

1×

intervals

Results

540.0ms	8000×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 286 to 221 computations (22.7% saved)

Details

analyze109.0ms (1.7%)

sample25.0ms (0.4%)

simplify204.0ms (3.2%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite57.0ms (0.9%)

series641.0ms (10%)

simplify82.0ms (1.3%)

prune227.0ms (3.5%)

localize15.0ms (0.2%)

rewrite57.0ms (0.9%)

series508.0ms (7.9%)

simplify109.0ms (1.7%)

prune315.0ms (4.9%)

localize23.0ms (0.4%)

rewrite87.0ms (1.4%)

series843.0ms (13.2%)

simplify97.0ms (1.5%)

prune431.0ms (6.7%)

localize19.0ms (0.3%)

rewrite87.0ms (1.4%)

series935.0ms (14.6%)

simplify109.0ms (1.7%)

prune445.0ms (6.9%)

regimes60.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample901.0ms (14.1%)

Profiling