Details

analyze693.0ms (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
4.0ms	106×	body	128	invalid

Compiler

Compiled 27 to 27 computations (0% saved)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	665	19
1	665	19

prune3.0ms (0.1%)

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

Merged error: 6.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
6.4b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`cancel-sign-sub-inv_binary64`
8×	`associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64`
1×	`diff-log_binary64` `associate-l_binary64` `difference-of-squares_binary64` `*-commutative_binary64`

Counts

2 → 49

Calls

2 calls:

10.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
6.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))

series232.0ms (5.2%)

Counts

2 → 6

Calls

2 calls:

123.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
109.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4970	973
1	4970	973

prune124.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	6	56

Merged error: 2.0b

Counts

56 → 6

Compiler

Compiled 2446 to 1398 computations (42.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.8b	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
6.4b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
6.4b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
6.4b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cancel-sign-sub-inv_binary64`
17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`sub-neg_binary64` `associate-*r/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`associate-l_binary64` `difference-of-squares_binary64` `cbrt-prod_binary64` `*-commutative_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 100

Calls

4 calls:

11.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
11.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
11.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
4.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))

series563.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
98.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
98.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
97.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4976	1906
1	4976	1906

prune177.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	112	6	118

Merged error: 2.0b

Counts

118 → 6

Compiler

Compiled 5561 to 2306 computations (58.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
0.2b	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
6.4b	(sqrt.f64 (-.f64 (*.f64 z z) t))
6.4b	(sqrt.f64 (-.f64 (*.f64 z z) t))

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
14×	`associate-r_binary64`
10×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64`
9×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `frac-times_binary64`
2×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
11.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
7.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
5.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

series313.0ms (7%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
104.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
53.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
50.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4938	1705
1	4938	1705

prune123.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Merged error: 2.0b

Counts

107 → 7

Compiler

Compiled 3129 to 1172 computations (62.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 z z) t))))
6.4b	(sqrt.f64 (-.f64 (*.f64 z z) t))
6.4b	(sqrt.f64 (-.f64 (*.f64 z z) t))
6.4b	(sqrt.f64 (-.f64 (*.f64 z z) t))

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`sqrt-prod_binary64`
67×	`add-sqr-sqrt_binary64`
35×	`sqrt-pow1_binary64`
30×	`pow1_binary64` `sqrt-div_binary64`
19×	`*-un-lft-identity_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64`
16×	`swap-sqr_binary64`
11×	`rem-sqrt-square_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `pow-prod-up_binary64` `unswap-sqr_binary64` `flip--_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `sqr-abs_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 z z) t))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
5.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
5.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

series227.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
55.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 z z) t))))
54.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
53.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4996	2068
1	4996	2068

prune167.0ms (3.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	150	7	157

Merged error: 2.0b

Counts

157 → 7

Compiler

Compiled 4931 to 1325 computations (73.1% saved)

regimes314.0ms (7%)

Compiler: Compiled 1969 to 1359 computations (31% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	297	54
1	297	54

end0.0ms (0%)

sample910.0ms (20.3%)

Algorithm

1×

intervals

Results

314.0ms	8000×	body	128	valid
131.0ms	3047×	body	128	invalid

Compiler

Compiled 212 to 146 computations (31.1% saved)

Details

analyze693.0ms (15.5%)

sample26.0ms (0.6%)

simplify58.0ms (1.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite20.0ms (0.5%)

series232.0ms (5.2%)

simplify82.0ms (1.8%)

prune124.0ms (2.8%)

localize14.0ms (0.3%)

rewrite55.0ms (1.2%)

series563.0ms (12.6%)

simplify71.0ms (1.6%)

prune177.0ms (3.9%)

localize12.0ms (0.3%)

rewrite51.0ms (1.1%)

series313.0ms (7%)

simplify70.0ms (1.6%)

prune123.0ms (2.7%)

localize18.0ms (0.4%)

rewrite55.0ms (1.2%)

series227.0ms (5.1%)

simplify82.0ms (1.8%)

prune167.0ms (3.7%)

regimes314.0ms (7%)

bsearch1.0ms (0%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample910.0ms (20.3%)

Profiling