Details

analyze659.0ms (10.1%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample19.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	26×	body	128	invalid

Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify232.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	1166	13
1	1166	13

prune5.0ms (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: 5.0b

Counts

2 → 2

Compiler

Compiled 49 to 47 computations (4.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (-.f64 y t))
0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
5.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

rewrite74.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64_15565`
180×	`add-sqr-sqrt_binary64_15581`
171×	`*-un-lft-identity_binary64_15559`
121×	`add-cube-cbrt_binary64_15594`
67×	`associate-r_binary64_15499`
25×	`distribute-lft-out--_binary64_15511` `difference-of-squares_binary64_15528`
24×	`associate-/l*_binary64_15504`
19×	`add-cbrt-cube_binary64_15595` `add-exp-log_binary64_15597`
16×	`associate-/r/_binary64_15505`
10×	`div-inv_binary64_15556`
8×	`flip--_binary64_15534` `associate-/r*_binary64_15503` `flip3--_binary64_15563`
7×	`cbrt-undiv_binary64_15593` `div-exp_binary64_15610`
5×	`pow1_binary64_15620`
3×	`prod-exp_binary64_15608` `add-log-exp_binary64_15598` `associate-l_binary64_15500` `cbrt-unprod_binary64_15592` `unswap-sqr_binary64_15527`
2×	`frac-2neg_binary64_15570` `clear-num_binary64_15558`
1×	`associate-r/_binary64_15501` `pow-prod-down_binary64_15630` `associate-/l/_binary64_15506` `-commutative_binary64_15490`

Counts

3 → 228

Calls

3 calls:

27.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
14.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
6.0ms	(/.f64 2 (-.f64 y t))

series335.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

163.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
119.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
54.0ms	(/.f64 2 (-.f64 y t))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4957	4396
1	4957	4396

prune546.0ms (8.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	229	8	237
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	229	10	239

Merged error: 0.0b

Counts

239 → 10

Compiler

Compiled 9970 to 6474 computations (35.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
1.1b	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64_15590`
54×	`add-sqr-sqrt_binary64_15581`
51×	`*-un-lft-identity_binary64_15559`
47×	`times-frac_binary64_15565`
33×	`add-cube-cbrt_binary64_15594`
22×	`add-exp-log_binary64_15597`
14×	`add-cbrt-cube_binary64_15595`
9×	`distribute-lft-out--_binary64_15511` `difference-of-squares_binary64_15528` `prod-exp_binary64_15608` `cbrt-unprod_binary64_15592`
6×	`pow1_binary64_15620` `associate-/r/_binary64_15505`
5×	`associate-r_binary64_15499`
4×	`div-inv_binary64_15556` `cbrt-undiv_binary64_15593` `add-log-exp_binary64_15598` `div-exp_binary64_15610`
3×	`flip--_binary64_15534` `cbrt-div_binary64_15591` `pow1/3_binary64_15641` `flip3--_binary64_15563` `associate-l_binary64_15500`
2×	`unswap-sqr_binary64_15527`
1×	`associate-r/_binary64_15501` `pow-prod-down_binary64_15630` `-commutative_binary64_15490`

Counts

4 → 120

Calls

4 calls:

27.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
6.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
6.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
6.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))

series1.3s (19.9%)

Counts

4 → 12

Calls

4 calls:

491.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
281.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
266.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
255.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4956	2993
1	4956	2993

prune258.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	132	10	142

Merged error: 0b

Counts

142 → 10

Compiler

Compiled 5567 to 2937 computations (47.2% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
0.6b	(cbrt.f64 (/.f64 2 (-.f64 y t)))
1.0b	(cbrt.f64 2)
1.1b	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`cbrt-prod_binary64_15590`
39×	`add-sqr-sqrt_binary64_15581`
37×	`*-un-lft-identity_binary64_15559`
33×	`add-exp-log_binary64_15597`
31×	`times-frac_binary64_15565`
25×	`add-cube-cbrt_binary64_15594`
19×	`add-cbrt-cube_binary64_15595`
14×	`prod-exp_binary64_15608` `cbrt-unprod_binary64_15592`
8×	`cbrt-undiv_binary64_15593` `div-exp_binary64_15610`
6×	`distribute-lft-out--_binary64_15511` `difference-of-squares_binary64_15528` `pow1_binary64_15620`
5×	`associate-r_binary64_15499`
4×	`add-log-exp_binary64_15598` `associate-/r/_binary64_15505`
3×	`div-inv_binary64_15556` `pow1/3_binary64_15641` `associate-l_binary64_15500`
2×	`flip--_binary64_15534` `cbrt-div_binary64_15591` `flip3--_binary64_15563`
1×	`associate-r/_binary64_15501` `pow-prod-down_binary64_15630` `-commutative_binary64_15490` `unswap-sqr_binary64_15527`

Counts

4 → 104

Calls

4 calls:

25.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
6.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
5.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
1.0ms	(cbrt.f64 2)

series1.0s (15.7%)

Counts

4 → 10

Calls

4 calls:

491.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (/.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
265.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
263.0ms	(cbrt.f64 (/.f64 2 (-.f64 y t)))
0.0ms	(cbrt.f64 2)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5006	2695

prune192.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	114	10	124

Merged error: 0b

Counts

124 → 10

Compiler

Compiled 4554 to 2265 computations (50.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 2 (-.f64 y t))
0.2b	(*.f64 x (/.f64 2 (-.f64 y t)))
4.1b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_15581`
39×	`*-un-lft-identity_binary64_15559`
34×	`times-frac_binary64_15565`
25×	`add-cube-cbrt_binary64_15594`
21×	`associate-r_binary64_15499`
19×	`add-cbrt-cube_binary64_15595` `add-exp-log_binary64_15597`
8×	`associate-/r*_binary64_15503`
7×	`distribute-lft-out--_binary64_15511` `difference-of-squares_binary64_15528`
6×	`cbrt-undiv_binary64_15593` `div-exp_binary64_15610`
5×	`pow1_binary64_15620`
4×	`prod-exp_binary64_15608` `associate-/l*_binary64_15504` `associate-/r/_binary64_15505` `cbrt-unprod_binary64_15592`
3×	`div-inv_binary64_15556` `add-log-exp_binary64_15598` `associate-l_binary64_15500`
2×	`flip--_binary64_15534` `frac-2neg_binary64_15570` `associate-*r/_binary64_15501` `flip3--_binary64_15563` `clear-num_binary64_15558` `unswap-sqr_binary64_15527`
1×	`pow-prod-down_binary64_15630` `associate-/l/_binary64_15506` `*-commutative_binary64_15490`

Counts

3 → 101

Calls

3 calls:

12.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
9.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
6.0ms	(/.f64 2 (-.f64 y t))

series299.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

160.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
82.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
58.0ms	(/.f64 2 (-.f64 y t))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5126	1404

prune127.0ms (2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	5	2	7
Picked	0	1	1
Done	0	2	2
Total	111	9	120

Merged error: 0b

Counts

120 → 9

Compiler

Compiled 2255 to 1367 computations (39.4% saved)

regimes110.0ms (1.7%)

Compiler: Compiled 648 to 604 computations (6.8% saved)

bsearch30.0ms (0.5%)

Steps

Iters	Range		Point
5	13411970.716102028	27055041.208227757	15670887.655105175
10	-5.7179285168183544e-213	-3.113917599530434e-225	-4.9660709412788435e-216

Compiler

Compiled 3 to 6 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46

end0.0ms (0%)

sample782.0ms (12%)

Algorithm

1×

intervals

Results

304.0ms	8000×	body	128	valid
28.0ms	708×	body	128	invalid

Compiler

Compiled 220 to 175 computations (20.5% saved)

Details

analyze659.0ms (10.1%)

sample19.0ms (0.3%)

simplify232.0ms (3.6%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite74.0ms (1.1%)

series335.0ms (5.2%)

simplify89.0ms (1.4%)

prune546.0ms (8.4%)

localize15.0ms (0.2%)

rewrite61.0ms (0.9%)

series1.3s (19.9%)

simplify107.0ms (1.6%)

prune258.0ms (4%)

localize19.0ms (0.3%)

rewrite51.0ms (0.8%)

series1.0s (15.7%)

simplify75.0ms (1.2%)

prune192.0ms (2.9%)

localize7.0ms (0.1%)

rewrite35.0ms (0.5%)

series299.0ms (4.6%)

simplify55.0ms (0.8%)

prune127.0ms (2%)

regimes110.0ms (1.7%)

bsearch30.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample782.0ms (12%)

Profiling