Details

analyze259.0ms (4%)

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 20 to 13 computations (35% saved)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

785×	`distribute-rgt-neg-in_binary64`
770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
289×	`sub-neg_binary64`
232×	`associate-+l+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	29	25
2	50	25
3	138	25
4	374	25
5	1117	25
6	2839	25
7	5140	25

prune4.0ms (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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 57 to 36 computations (36.8% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite178.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

4 → 59

Calls

4 calls:

13.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
9.0ms	(.f64 4 (.f64 b b))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
6.0ms	(+.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 1430 to 623 computations (56.4% saved)

series283.0ms (4.4%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

124.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
74.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
40.0ms	(+.f64 (.f64 a a) (.f64 b b))
11.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1724 to 1354 computations (21.5% saved)

simplify222.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-l_binary64`
585×	`associate-r_binary64`
408×	`distribute-rgt-neg-in_binary64`
301×	`exp-prod_binary64`
242×	`distribute-rgt-in_binary64`

Counts

110 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1770
1	299	1632
2	858	1626
3	3568	1626
4	4705	1626
5	4956	1626
6	4881	1626

prune75.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

Counts

74 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
	16.6b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 4 (.f64 b b)) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) 3)) 1)
	0.6b	(-.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b))) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 950 to 484 computations (49.1% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4))
0.0b	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
2.1b	(.f64 (.f64 a a) (*.f64 b b))

rewrite238.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
21×	`add-exp-log_binary64`
18×	`add-log-exp_binary64`
17×	`pow-prod-down_binary64`

Counts

4 → 76

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
15.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4))
15.0ms	(.f64 (.f64 a a) (*.f64 b b))
9.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 2330 to 1238 computations (46.9% saved)

series336.0ms (5.2%)

Error

Counts

4 → 45

Calls

4 calls:

146.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4))
122.0ms	(+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b)))
33.0ms	(.f64 (.f64 a a) (*.f64 b b))
14.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1768 to 1384 computations (21.7% saved)

simplify136.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

787×	`distribute-rgt-in_binary64`
759×	`distribute-lft-in_binary64`
312×	`associate-+l+_binary64`
162×	`associate-l_binary64`
161×	`cancel-sign-sub-inv_binary64`

Counts

121 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	2453
1	325	2196
2	1232	2090
3	4977	2090

prune114.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Error

Counts

88 → 4

Alt Table

Status	Error	Program
	16.6b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.6b	(-.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 1477 to 856 computations (42% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
0.6b	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
10.6b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
10.6b	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

rewrite180.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 69

Calls

4 calls:

9.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
9.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
7.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
6.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 2534 to 860 computations (66.1% saved)

series478.0ms (7.4%)

Error

Counts

4 → 51

Calls

4 calls:

177.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
102.0ms	(pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)
80.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
79.0ms	(cbrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 3686 to 2704 computations (26.6% saved)

simplify248.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-l_binary64`
419×	`associate-r_binary64`
297×	`distribute-rgt-in_binary64`
271×	`log-prod_binary64`
262×	`distribute-lft-in_binary64`

Counts

120 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2194
1	298	2130
2	715	2127
3	2310	2122
4	4455	2122
5	4973	2122
6	4994	2122

prune127.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
▶	16.6b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.6b	(-.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 2083 to 868 computations (58.3% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))
0.2b	(pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)
1.3b	(.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4))
30.7b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3))

rewrite319.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`

Counts

4 → 88

Calls

4 calls:

29.0ms	(pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)
26.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3))
25.0ms	(+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))
24.0ms	(.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4))

Compiler

Compiled 3038 to 1999 computations (34.2% saved)

series534.0ms (8.3%)

Error

Counts

4 → 63

Calls

4 calls:

181.0ms	(pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)
120.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3))
91.0ms	(+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))
59.0ms	(.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4))

Compiler

Compiled 3383 to 2783 computations (17.7% saved)

simplify291.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

462×	`unswap-sqr_binary64`
288×	`associate-+r+_binary64`
280×	`cancel-sign-sub-inv_binary64`
269×	`associate-r_binary64`
266×	`exp-prod_binary64`

Counts

151 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5313
1	725	4914
2	2959	4886
3	4671	4886
4	4970	4886

prune192.0ms (3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	125	4	129

Error

Counts

129 → 4

Alt Table

Status	Error	Program
	16.6b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 (.f64 b b) (+.f64 (.f64 2 (.f64 a a)) 4)) (pow.f64 b 4))) 3)) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
	0.6b	(-.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (pow.f64 (cbrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 2)) (.f64 4 (*.f64 b b))) 1)
	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))) (pow.f64 a 4)) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 2549 to 1766 computations (30.7% saved)

regimes1.1s (16.4%)

Accuracy

Total 0.0b remaining (46.9%)

Threshold costs 0.0b (46.9%)

Compiler

Compiled 11961 to 8145 computations (31.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	26	31
2	27	31
3	25	31

end1.0ms (0%)

Compiler: Compiled 23 to 17 computations (26.1% saved)

sample961.0ms (14.9%)

Algorithm

1×

intervals

Results

592.0ms	8000×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 148 to 98 computations (33.8% saved)

Details

analyze259.0ms (4%)

sample42.0ms (0.6%)

simplify51.0ms (0.8%)

prune4.0ms (0.1%)

localize25.0ms (0.4%)

rewrite178.0ms (2.8%)

series283.0ms (4.4%)

simplify222.0ms (3.4%)

prune75.0ms (1.2%)

localize29.0ms (0.4%)

rewrite238.0ms (3.7%)

series336.0ms (5.2%)

simplify136.0ms (2.1%)

prune114.0ms (1.8%)

localize29.0ms (0.4%)

rewrite180.0ms (2.8%)

series478.0ms (7.4%)

simplify248.0ms (3.9%)

prune127.0ms (2%)

localize33.0ms (0.5%)

rewrite319.0ms (4.9%)

series534.0ms (8.3%)

simplify291.0ms (4.5%)

prune192.0ms (3%)

regimes1.1s (16.4%)

simplify9.0ms (0.1%)

end1.0ms (0%)

sample961.0ms (14.9%)

Profiling