Details

analyze989.0ms (18.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample67.0ms (1.2%)

Algorithm

1×

intervals

Results

36.0ms	120×	body	2048	valid
14.0ms	68×	body	1024	valid
5.0ms	38×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	18×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify163.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4955	21
1	4955	21

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.5b

Counts

2 → 1

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.2b	(.f64 5 (.f64 v v))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
19×	`*-un-lft-identity_binary64_2124`
18×	`times-frac_binary64_2130`
15×	`add-cube-cbrt_binary64_2159`
10×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`difference-of-squares_binary64_2093` `pow1_binary64_2185`
6×	`associate-/r*_binary64_2068`
4×	`difference-of-sqr-1_binary64_2094`
3×	`pow-prod-down_binary64_2195` `associate-/l_binary64_2069` `add-log-exp_binary64_2163` `associate-l*_binary64_2065` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `-commutative_binary64_2055` `acos-asin_binary64_2305` `associate-r*_binary64_2064` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

3 → 71

Calls

6 calls:

9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
6.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series79.0ms (1.5%)

Counts

3 → 12

Calls

3 calls:

30.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
26.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
23.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 238 to 220 computations (7.6% saved)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4931	1785
1	4931	1785

prune101.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Error

0.5b

Counts

84 → 3

Compiler

Compiled 1805 to 1161 computations (35.7% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.5b	(acos.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1)))
0.2b	(.f64 5 (.f64 v v))
0.0b	(.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1))
0.0b	(.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.5b	(acos.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_2146`
43×	`times-frac_binary64_2130` `*-un-lft-identity_binary64_2124`
30×	`associate-l_binary64_2065`
29×	`add-cube-cbrt_binary64_2159`
21×	`difference-of-sqr--1_binary64_2095`
16×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
11×	`pow1_binary64_2185`
7×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068` `sqr-pow_binary64_2096`
5×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`pow-prod-down_binary64_2195` `associate-/r/_binary64_2070` `add-log-exp_binary64_2163` `flip3-+_binary64_2127` `associate-r_binary64_2064` `flip-+_binary64_2098`
3×	`unswap-sqr_binary64_2092` `associate-/l*_binary64_2069`
2×	`cbrt-undiv_binary64_2158` `-commutative_binary64_2055` `associate-r/_binary64_2066` `frac-times_binary64_2134` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `acos-asin_binary64_2305` `associate-*l/_binary64_2067` `distribute-rgt-in_binary64_2074` `div-sub_binary64_2129` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 127

Calls

8 calls:

22.0ms	(.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1))
9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1))
6.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1)))
0.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1))

series134.0ms (2.5%)

Counts

4 → 18

Calls

4 calls:

47.0ms	(.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1))
31.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1))
29.0ms	(acos.f64 (.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (+.f64 (pow.f64 v 4) -1)) (+.f64 (.f64 v v) 1)))
26.0ms	(.f64 5 (.f64 v v))

Compiler

Compiled 438 to 388 computations (11.4% saved)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5068	3498

prune220.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Error

0.5b

Counts

148 → 3

Compiler

Compiled 4043 to 2729 computations (32.5% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.2b	(.f64 5 (.f64 v v))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
24×	`sqrt-prod_binary64_2140`
21×	`pow1_binary64_2185`
14×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204`
8×	`swap-sqr_binary64_2091`
6×	`associate-l_binary64_2065` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-up_binary64_2194`
4×	`unswap-sqr_binary64_2092` `rem-sqrt-square_binary64_2137` `add-log-exp_binary64_2163`
3×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
1×	`sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `acos-asin_binary64_2305` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `sqr-abs_binary64_2139` `cbrt-unprod_binary64_2157`

Counts

4 → 84

Calls

8 calls:

7.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))

series138.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
42.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
25.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
23.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 642 to 528 computations (17.8% saved)

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5552	2247

prune138.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Error

0.5b

Counts

99 → 5

Compiler

Compiled 3046 to 1932 computations (36.6% saved)

localize14.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.0b	(pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`sqrt-prod_binary64_2140`
63×	`add-sqr-sqrt_binary64_2146`
24×	`unswap-sqr_binary64_2092` `associate-r_binary64_2064`
18×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
16×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`associate-l_binary64_2065` `add-exp-log_binary64_2162`
7×	`pow1_binary64_2185`
6×	`add-cbrt-cube_binary64_2160`
4×	`add-log-exp_binary64_2163` `sqr-pow_binary64_2096`
3×	`prod-exp_binary64_2173`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`unpow3_binary64_2190` `pow-prod-up_binary64_2194` `cube-mult_binary64_2154` `pow-exp_binary64_2192` `*-commutative_binary64_2055` `acos-asin_binary64_2305` `pow-to-exp_binary64_2193` `cbrt-unprod_binary64_2157`

Counts

4 → 104

Calls

8 calls:

14.0ms	(.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))

series146.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
43.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
32.0ms	(.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))
25.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

Compiler

Compiled 714 to 600 computations (16% saved)

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4843	3934
1	4843	3934

prune216.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	115	6	121

Error

0.5b

Counts

121 → 6

Compiler

Compiled 4432 to 2928 computations (33.9% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	125	693
1	125	693

regimes133.0ms (2.4%)

Compiler: Compiled 1858 to 1332 computations (28.3% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.3%)

Compiler: Compiled 34 to 38 computations (-11.8% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.2%)

Compiler: Compiled 7 to 11 computations (-57.1% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

Accuracy

Total 0.0b remaining (4.3%)

Threshold costs 0.0b (4.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0%)

Compiler: Compiled 25 to 22 computations (12% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	37
1	49	37

end0.0ms (0%)

sample2.4s (43.9%)

Algorithm

1×

intervals

Results

1.2s	4031×	body	2048	valid
399.0ms	2005×	body	1024	valid
142.0ms	1005×	body	512	valid
43.0ms	453×	body	256	valid
27.0ms	504×	body	128	valid
1.0ms	2×	body	4096	valid
0.0ms	11×	body	128	nan

Compiler

Compiled 489 to 356 computations (27.2% saved)

Pareto

0.09280841848251867

Details

analyze989.0ms (18.2%)

sample67.0ms (1.2%)

simplify163.0ms (3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite21.0ms (0.4%)

series79.0ms (1.5%)

simplify81.0ms (1.5%)

prune101.0ms (1.9%)

localize12.0ms (0.2%)

rewrite51.0ms (0.9%)

series134.0ms (2.5%)

simplify67.0ms (1.2%)

prune220.0ms (4%)

localize14.0ms (0.2%)

rewrite20.0ms (0.4%)

series138.0ms (2.5%)

simplify72.0ms (1.3%)

prune138.0ms (2.5%)

localize14.0ms (0.3%)

rewrite34.0ms (0.6%)

series146.0ms (2.7%)

simplify79.0ms (1.5%)

prune216.0ms (4%)

simplify12.0ms (0.2%)

regimes133.0ms (2.4%)

bsearch0.0ms (0%)

regimes17.0ms (0.3%)

bsearch0.0ms (0%)

regimes10.0ms (0.2%)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

bsearch3.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.4s (43.9%)

Profiling