Details

analyze83.0ms (1.6%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify209.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5126	25

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: 0.2b

Counts

2 → 1

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
9×	`add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163` `add-sqr-sqrt_binary64_2146`
7×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
3×	`pow-prod-down_binary64_2195` `pow-unpow_binary64_2201` `unpow-prod-down_binary64_2203` `associate-l_binary64_2065` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`unswap-sqr_binary64_2092` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `-commutative_binary64_2055` `sqr-pow_binary64_2096` `unpow2_binary64_2189` `pow-to-exp_binary64_2193` `associate-r*_binary64_2064`

Counts

4 → 59

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(+.f64 (.f64 a a) (.f64 b b))

series216.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
51.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
37.0ms	(+.f64 (.f64 a a) (.f64 b b))
36.0ms	(.f64 4 (.f64 b b))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4923	1108
1	4923	1108

prune275.0ms (5.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0b

Counts

72 → 3

Compiler

Compiled 1645 to 786 computations (52.2% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
1.7b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
18×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
12×	`add-log-exp_binary64_2163`
6×	`sum-log_binary64_2215`
5×	`add-sqr-sqrt_binary64_2146`
4×	`add-cube-cbrt_binary64_2159` `associate-l_binary64_2065` `*-un-lft-identity_binary64_2124`
2×	`-commutative_binary64_2055` `associate-r*_binary64_2064`
1×	`unswap-sqr_binary64_2092` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `associate-+l+_binary64_2057` `flip-+_binary64_2098`

Counts

3 → 61

Calls

3 calls:

23.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
11.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
6.0ms	(.f64 4 (.f64 b b))

series173.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
53.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
36.0ms	(.f64 4 (.f64 b b))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4958	1194
1	4958	1194

prune95.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	70	3	73

Merged error: 0b

Counts

73 → 3

Compiler

Compiled 2050 to 1365 computations (33.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 b b) 4)
0.2b	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
30.0b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
13×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
12×	`cbrt-prod_binary64_2155`
11×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
10×	`add-cbrt-cube_binary64_2160`
9×	`unpow-prod-down_binary64_2203`
6×	`pow-unpow_binary64_2201` `cube-prod_binary64_2152`
4×	`add-log-exp_binary64_2163` `cube-div_binary64_2153`
3×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `sqr-pow_binary64_2096` `associate-r_binary64_2064` `cbrt-unprod_binary64_2157`
2×	`unpow3_binary64_2190` `cbrt-div_binary64_2156` `cube-mult_binary64_2154` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `pow-to-exp_binary64_2193` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`unswap-sqr_binary64_2092` `rem-cbrt-cube_binary64_2148` `-commutative_binary64_2055` `associate-l*_binary64_2065` `pow1/3_binary64_2206` `unpow2_binary64_2189` `rem-cube-cbrt_binary64_2147`

Counts

4 → 85

Calls

4 calls:

11.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3)
9.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3))
7.0ms	(.f64 (.f64 b b) 4)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series826.0ms (16.2%)

Counts

4 → 12

Calls

4 calls:

661.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3)
84.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)) 3))
47.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
33.0ms	(.f64 (.f64 b b) 4)

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4954	2271
1	4954	2271

prune114.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Merged error: 0b

Counts

100 → 3

Compiler

Compiled 2636 to 1354 computations (48.6% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
2.0b	(.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4))
2.8b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))))
45.2b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (.f64 64 (pow.f64 b 6))) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))

rewrite71.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_2162`
27×	`*-un-lft-identity_binary64_2124`
18×	`prod-exp_binary64_2173`
17×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
15×	`add-cbrt-cube_binary64_2160`
12×	`times-frac_binary64_2130`
9×	`add-log-exp_binary64_2163`
8×	`associate-l_binary64_2065`
6×	`unpow-prod-down_binary64_2203` `cbrt-unprod_binary64_2157`
5×	`distribute-lft-out_binary64_2075` `pow1_binary64_2185`
4×	`pow-exp_binary64_2192` `associate-/r*_binary64_2068` `pow-to-exp_binary64_2193`
3×	`pow-unpow_binary64_2201` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-/r/_binary64_2070` `sum-log_binary64_2215` `associate-+r+_binary64_2056` `sqr-pow_binary64_2096` `unpow2_binary64_2189` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `associate-+r-_binary64_2058` `pow-pow_binary64_2196` `-commutative_binary64_2055` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-r*_binary64_2064` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 98

Calls

4 calls:

22.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (.f64 64 (pow.f64 b 6))) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))
13.0ms	(.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4))
13.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series1.1s (21.5%)

Counts

4 → 12

Calls

4 calls:

540.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (.f64 64 (pow.f64 b 6))) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))
416.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (-.f64 (.f64 16 (pow.f64 b 4)) (.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))))
93.0ms	(.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4))
46.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5056	5411

prune281.0ms (5.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	110	3	113

Merged error: 0b

Counts

113 → 3

Compiler

Compiled 6841 to 3296 computations (51.8% saved)

regimes252.0ms (4.9%)

Compiler: Compiled 2984 to 2064 computations (30.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	37
1	35	37

end0.0ms (0%)

sample880.0ms (17.2%)

Algorithm

1×

intervals

Results

359.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 423 to 295 computations (30.3% saved)

Details

analyze83.0ms (1.6%)

sample19.0ms (0.4%)

simplify209.0ms (4.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite29.0ms (0.6%)

series216.0ms (4.2%)

simplify76.0ms (1.5%)

prune275.0ms (5.4%)

localize15.0ms (0.3%)

rewrite47.0ms (0.9%)

series173.0ms (3.4%)

simplify79.0ms (1.5%)

prune95.0ms (1.9%)

localize13.0ms (0.3%)

rewrite40.0ms (0.8%)

series826.0ms (16.2%)

simplify86.0ms (1.7%)

prune114.0ms (2.2%)

localize30.0ms (0.6%)

rewrite71.0ms (1.4%)

series1.1s (21.5%)

simplify87.0ms (1.7%)

prune281.0ms (5.5%)

regimes252.0ms (4.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample880.0ms (17.2%)

Profiling