Details

analyze134.0ms (2.5%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify240.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5070	43

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 58 to 38 computations (34.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64_2204` `add-sqr-sqrt_binary64_2165` `add-exp-log_binary64_2181` `*-un-lft-identity_binary64_2143`
14×	`add-cbrt-cube_binary64_2179`
10×	`associate-r_binary64_2083` `add-cube-cbrt_binary64_2178`
6×	`add-log-exp_binary64_2182` `distribute-rgt-in_binary64_2093` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `cancel-sign-sub-inv_binary64_2109` `distribute-lft-in_binary64_2092`
4×	`associate-*r/_binary64_2085`
3×	`pow-unpow_binary64_2220` `unpow-prod-down_binary64_2222`
2×	`sub-neg_binary64_2136` `associate-l_binary64_2084` `associate-+r+_binary64_2075` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074` `difference-of-squares_binary64_2112`
1×	`unpow2_binary64_2208` `+-commutative_binary64_2073` `flip--_binary64_2118` `distribute-lft-out--_binary64_2095` `pow-to-exp_binary64_2212` `sum-log_binary64_2234` `flip3--_binary64_2147` `distribute-lft-out_binary64_2094` `pow-pow_binary64_2215` `sqr-pow_binary64_2115` `pow-exp_binary64_2211`

Counts

4 → 87

Calls

4 calls:

11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series327.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
70.0ms	(.f64 (.f64 a a) (-.f64 1 a))
55.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
52.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5074	1789

prune202.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	2	100

Merged error: 0.0b

Counts

100 → 2

Compiler

Compiled 4809 to 2590 computations (46.1% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
1.4b	(.f64 (.f64 b b) (+.f64 3 a))
2.8b	(.f64 (.f64 b b) (*.f64 a a))

rewrite90.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_2204`
32×	`associate-*r/_binary64_2085`
26×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
20×	`pow-prod-down_binary64_2214` `frac-add_binary64_2151`
14×	`cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `flip3-+_binary64_2146` `flip-+_binary64_2117`
13×	`add-sqr-sqrt_binary64_2165` `add-log-exp_binary64_2182` `*-un-lft-identity_binary64_2143`
11×	`associate-r_binary64_2083`
8×	`add-cube-cbrt_binary64_2178`
6×	`distribute-rgt-in_binary64_2093` `sum-log_binary64_2234` `cancel-sign-sub-inv_binary64_2109` `distribute-lft-in_binary64_2092`
5×	`flip--_binary64_2118` `flip3--_binary64_2147`
4×	`pow-plus_binary64_2206` `pow-prod-up_binary64_2213`
3×	`associate-l_binary64_2084` `unswap-sqr_binary64_2111` `*-commutative_binary64_2074`
2×	`pow2_binary64_2224` `sub-neg_binary64_2136` `pow-sqr_binary64_2116` `associate-+r+_binary64_2075` `difference-of-squares_binary64_2112`
1×	`+-commutative_binary64_2073` `distribute-lft-out--_binary64_2095` `associate-+l+_binary64_2076` `distribute-lft-out_binary64_2094`

Counts

4 → 113

Calls

4 calls:

31.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(.f64 (.f64 b b) (*.f64 a a))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series331.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
71.0ms	(.f64 (.f64 a a) (-.f64 1 a))
52.0ms	(.f64 (.f64 b b) (+.f64 3 a))
50.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4942	4559
1	4942	4559

prune301.0ms (5.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Merged error: 0.0b

Counts

127 → 2

Compiler

Compiled 6527 to 3838 computations (41.2% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (pow.f64 (.f64 b a) 2))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.1b	(pow.f64 (*.f64 b a) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_2181`
20×	`add-sqr-sqrt_binary64_2165`
17×	`pow1_binary64_2204`
16×	`associate-r_binary64_2083` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
12×	`prod-exp_binary64_2192`
11×	`add-cube-cbrt_binary64_2178`
7×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214`
6×	`cancel-sign-sub-inv_binary64_2109`
5×	`distribute-rgt-in_binary64_2093` `associate-l_binary64_2084` `unswap-sqr_binary64_2111` `distribute-lft-in_binary64_2092`
4×	`add-log-exp_binary64_2182` `associate-*r/_binary64_2085` `pow-exp_binary64_2211`
3×	`unpow2_binary64_2208` `pow-unpow_binary64_2220` `sqr-pow_binary64_2115` `*-commutative_binary64_2074`
2×	`unpow-prod-down_binary64_2222` `sub-neg_binary64_2136` `pow-to-exp_binary64_2212` `pow-pow_binary64_2215` `difference-of-squares_binary64_2112`
1×	`flip--_binary64_2118` `distribute-lft-out--_binary64_2095` `flip3--_binary64_2147` `distribute-lft-out_binary64_2094` `flip3-+_binary64_2146` `flip-+_binary64_2117`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(.f64 2 (pow.f64 (.f64 b a) 2))
4.0ms	(pow.f64 (*.f64 b a) 2)

series214.0ms (4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (.f64 a a) (-.f64 1 a))
52.0ms	(.f64 2 (pow.f64 (.f64 b a) 2))
51.0ms	(.f64 (.f64 b b) (+.f64 3 a))
42.0ms	(pow.f64 (*.f64 b a) 2)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5261	1191

prune194.0ms (3.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	111	2	113

Merged error: 0.0b

Counts

113 → 2

Compiler

Compiled 4296 to 2740 computations (36.2% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
0.3b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)
1.4b	(.f64 (.f64 b b) (+.f64 3 a))
31.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_2143`
14×	`add-sqr-sqrt_binary64_2165`
13×	`add-cube-cbrt_binary64_2178`
12×	`cbrt-prod_binary64_2174`
11×	`pow1_binary64_2204` `add-exp-log_binary64_2181`
10×	`add-cbrt-cube_binary64_2179`
9×	`unpow-prod-down_binary64_2222`
6×	`pow-unpow_binary64_2220` `cube-prod_binary64_2171`
4×	`add-log-exp_binary64_2182` `associate-r_binary64_2083` `cube-div_binary64_2172`
3×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `flip3-+_binary64_2146` `sqr-pow_binary64_2115` `flip-+_binary64_2117`
2×	`cube-mult_binary64_2173` `pow-to-exp_binary64_2212` `pow-pow_binary64_2215` `associate-*r/_binary64_2085` `unpow3_binary64_2209` `cbrt-div_binary64_2175` `pow-exp_binary64_2211`
1×	`unpow2_binary64_2208` `distribute-rgt-in_binary64_2093` `rem-cbrt-cube_binary64_2167` `associate-l_binary64_2084` `distribute-lft-out_binary64_2094` `unswap-sqr_binary64_2111` `*-commutative_binary64_2074` `distribute-lft-in_binary64_2092` `rem-cube-cbrt_binary64_2166` `pow1/3_binary64_2225`

Counts

4 → 90

Calls

4 calls:

10.0ms	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
10.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)

series1.4s (26.6%)

Counts

4 → 12

Calls

4 calls:

1.2s	(pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3)
145.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (+.f64 3 a)) (-.f64 (.f64 a a) (pow.f64 a 3))))) 3))
56.0ms	(.f64 (.f64 b b) (+.f64 3 a))
47.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4876	3619
1	4876	3619

prune177.0ms (3.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	102	2	104

Merged error: 0.0b

Counts

104 → 2

Compiler

Compiled 4333 to 2319 computations (46.5% saved)

regimes213.0ms (3.9%)

Compiler: Compiled 2951 to 1863 computations (36.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	52
1	54	52

end0.0ms (0%)

sample1.0s (18.7%)

Algorithm

1×

intervals

Results

494.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 521 to 335 computations (35.7% saved)

Details

analyze134.0ms (2.5%)

sample23.0ms (0.4%)

simplify240.0ms (4.5%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite46.0ms (0.9%)

series327.0ms (6.1%)

simplify58.0ms (1.1%)

prune202.0ms (3.8%)

localize22.0ms (0.4%)

rewrite90.0ms (1.7%)

series331.0ms (6.1%)

simplify98.0ms (1.8%)

prune301.0ms (5.6%)

localize21.0ms (0.4%)

rewrite44.0ms (0.8%)

series214.0ms (4%)

simplify55.0ms (1%)

prune194.0ms (3.6%)

localize21.0ms (0.4%)

rewrite47.0ms (0.9%)

series1.4s (26.6%)

simplify68.0ms (1.3%)

prune177.0ms (3.3%)

regimes213.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (18.7%)

Profiling