Details

analyze561.0ms (9.9%)

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
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample56.0ms (1%)

Algorithm

1×

intervals

Results

20.0ms	53×	body	1024	valid
9.0ms	153×	body	128	valid
6.0ms	28×	body	512	valid
5.0ms	7×	body	2048	valid
3.0ms	8×	body	1024	invalid
2.0ms	15×	body	256	valid
1.0ms	5×	body	512	invalid
0.0ms	6×	body	128	nan
0.0ms	3×	body	256	invalid
0.0ms	6×	body	128	invalid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4926	13
1	4926	13

prune7.0ms (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: 10.7b

Counts

2 → 2

Compiler

Compiled 49 to 34 computations (30.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
0.1b	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
10.5b	(log.f64 (/.f64 x (+.f64 x y)))

rewrite88.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

261×	`times-frac_binary64`
221×	`*-un-lft-identity_binary64`
198×	`log-prod_binary64`
149×	`add-sqr-sqrt_binary64`
147×	`add-cube-cbrt_binary64`
144×	`exp-sum_binary64`
90×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
42×	`associate-/l*_binary64`
37×	`distribute-lft-out_binary64`
24×	`associate-/r/_binary64`
13×	`div-inv_binary64`
12×	`flip3-+_binary64` `add-exp-log_binary64` `flip-+_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64`
3×	`associate-l_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `log-div_binary64` `*-commutative_binary64`

Counts

4 → 288

Calls

4 calls:

19.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
11.0ms	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
6.0ms	(log.f64 (/.f64 x (+.f64 x y)))
6.0ms	(/.f64 x (+.f64 x y))

series492.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
128.0ms	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
67.0ms	(log.f64 (/.f64 x (+.f64 x y)))
51.0ms	(/.f64 x (+.f64 x y))

simplify132.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4992	6852
1	4992	6852

prune330.0ms (5.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	299	3	302

Merged error: 0.0b

Counts

302 → 3

Compiler

Compiled 7740 to 2225 computations (71.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
3.6b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
3.6b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`log-prod_binary64` `cbrt-prod_binary64`
84×	`*-un-lft-identity_binary64` `times-frac_binary64`
60×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
2×	`flip3-+_binary64` `pow1/3_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 140

Calls

4 calls:

9.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
9.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series580.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt.f64 x)
150.0ms	(cbrt.f64 x)
139.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))
138.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4921	3356
1	4921	3356

prune174.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Merged error: 0.0b

Counts

155 → 3

Compiler

Compiled 4864 to 1475 computations (69.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (exp.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y))))) (/.f64 1 x))
0.0b	(/.f64 x (+.f64 x y))
0.1b	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
10.5b	(log.f64 (/.f64 x (+.f64 x y)))

rewrite77.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
102×	`log-prod_binary64`
97×	`times-frac_binary64`
63×	`add-cube-cbrt_binary64`
48×	`exp-sum_binary64`
42×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
19×	`distribute-lft-out_binary64`
17×	`associate-r_binary64`
16×	`unswap-sqr_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
10×	`pow1_binary64`
7×	`div-inv_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `prod-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `un-div-inv_binary64` `log-div_binary64`

Counts

4 → 200

Calls

4 calls:

32.0ms	(.f64 (exp.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y))))) (/.f64 1 x))
10.0ms	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
6.0ms	(/.f64 x (+.f64 x y))
6.0ms	(log.f64 (/.f64 x (+.f64 x y)))

series472.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(.f64 (exp.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y))))) (/.f64 1 x))
124.0ms	(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
61.0ms	(log.f64 (/.f64 x (+.f64 x y)))
45.0ms	(/.f64 x (+.f64 x y))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	3818
1	4954	3818

prune173.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	212	3	215

Merged error: 0.0b

Counts

215 → 3

Compiler

Compiled 4272 to 1405 computations (67.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
3×	`associate-/r_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-exp-log_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `exp-neg_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

series43.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

43.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5150	428

prune27.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	32	3	35

Merged error: 0b

Counts

35 → 3

Compiler

Compiled 469 to 190 computations (59.5% saved)

regimes30.0ms (0.5%)

Compiler: Compiled 92 to 68 computations (26.1% saved)

bsearch64.0ms (1.1%)

Steps

Iters	Range		Point
7	0.013144348059336532	0.2887554185124614	0.28438769866631414
10	-13.231765455334582	-2.4201914395149656e-12	-12.735787451030035

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	73
1	38	73

end0.0ms (0%)

sample1.9s (33.1%)

Algorithm

1×

intervals

Results

664.0ms	1733×	body	1024	valid
267.0ms	4518×	body	128	valid
237.0ms	1035×	body	512	valid
118.0ms	167×	body	2048	valid
78.0ms	547×	body	256	valid
65.0ms	193×	body	1024	invalid
50.0ms	224×	body	512	invalid
19.0ms	144×	body	256	invalid
12.0ms	189×	body	128	invalid
8.0ms	189×	body	128	nan

Compiler

Compiled 146 to 93 computations (36.3% saved)

Details

analyze561.0ms (9.9%)

sample56.0ms (1%)

simplify52.0ms (0.9%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite88.0ms (1.6%)

series492.0ms (8.7%)

simplify132.0ms (2.3%)

prune330.0ms (5.8%)

localize14.0ms (0.2%)

rewrite40.0ms (0.7%)

series580.0ms (10.3%)

simplify112.0ms (2%)

prune174.0ms (3.1%)

localize10.0ms (0.2%)

rewrite77.0ms (1.4%)

series472.0ms (8.3%)

simplify105.0ms (1.9%)

prune173.0ms (3.1%)

localize4.0ms (0.1%)

rewrite8.0ms (0.1%)

series43.0ms (0.8%)

simplify117.0ms (2.1%)

prune27.0ms (0.5%)

regimes30.0ms (0.5%)

bsearch64.0ms (1.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (33.1%)

Profiling