Details

analyze532.0ms (8.5%)

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
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	192×	body	128	valid
6.0ms	31×	body	1024	valid
4.0ms	28×	body	1024	nan
3.0ms	20×	body	512	valid
1.0ms	12×	body	512	nan
1.0ms	11×	body	256	valid
1.0ms	2×	body	2048	valid
0.0ms	10×	body	128	nan
0.0ms	5×	body	256	nan

Compiler

Compiled 25 to 25 computations (0% saved)

simplify343.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (333.0ms)

Iter	Nodes	Cost
0	5118	18

prune2.0ms (0%)

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: 17.0b

Counts

2 → 1

Compiler

Compiled 24 to 22 computations (8.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
0.0b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
2.6b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
3.8b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite96.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
49×	`difference-of-squares_binary64`
40×	`cancel-sign-sub-inv_binary64`
32×	`add-cube-cbrt_binary64`
29×	`distribute-lft-out--_binary64`
16×	`log-prod_binary64`
8×	`associate--r+_binary64`
7×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
5×	`associate-/l*_binary64`
4×	`associate-/r/_binary64` `log-div_binary64`
3×	`associate--r-_binary64` `log-pow_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`

Counts

4 → 159

Calls

4 calls:

25.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
23.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
20.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
10.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

series364.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
116.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
81.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
50.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5416	3441

prune702.0ms (11.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	5	172

Merged error: 0.0b

Counts

172 → 5

Compiler

Compiled 12651 to 9412 computations (25.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (-.f64 1 y))
0.2b	(cbrt.f64 (-.f64 1 y))
3.8b	(log.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y))))))
9.4b	(-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y)))))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64`
3×	`log-prod_binary64`
2×	`pow1/3_binary64` `distribute-lft-out--_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `log-pow_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y)))))
4.0ms	(cbrt.f64 (-.f64 1 y))
4.0ms	(log.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y))))))
4.0ms	(cbrt.f64 (-.f64 1 y))

series249.0ms (4%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(log.f64 (-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y))))))
66.0ms	(-.f64 1 (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (/.f64 (-.f64 x y) (cbrt.f64 (-.f64 1 y)))))
42.0ms	(cbrt.f64 (-.f64 1 y))
41.0ms	(cbrt.f64 (-.f64 1 y))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6039	1193

prune101.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	70	5	75

Merged error: 0.0b

Counts

75 → 5

Compiler

Compiled 1950 to 1435 computations (26.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
0.0b	(log.f64 (/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
0.1b	(/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
2.6b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))

rewrite105.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`add-sqr-sqrt_binary64`
145×	`*-un-lft-identity_binary64`
124×	`times-frac_binary64`
67×	`difference-of-squares_binary64`
54×	`add-cube-cbrt_binary64`
36×	`cancel-sign-sub-inv_binary64`
32×	`distribute-lft-out--_binary64`
30×	`log-prod_binary64`
14×	`associate-/r*_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64`
3×	`div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `log-pow_binary64` `log-div_binary64`

Counts

4 → 201

Calls

4 calls:

27.0ms	(/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
23.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
23.0ms	(log.f64 (/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
10.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

series406.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(log.f64 (/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
127.0ms	(/.f64 (exp.f64 1) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
82.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
52.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5038	5428

prune298.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	214	4	218

Merged error: 0b

Counts

218 → 4

Compiler

Compiled 5023 to 3449 computations (31.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
2.6b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
3.6b	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
3.6b	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

rewrite111.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`add-sqr-sqrt_binary64`
102×	`*-un-lft-identity_binary64`
72×	`cancel-sign-sub-inv_binary64`
68×	`times-frac_binary64`
48×	`difference-of-squares_binary64`
32×	`add-cube-cbrt_binary64`
26×	`distribute-lft-out--_binary64`
22×	`log-prod_binary64`
16×	`cbrt-prod_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `flip--_binary64`
4×	`cbrt-div_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `log-div_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `div-sub_binary64` `div-inv_binary64`

Counts

4 → 152

Calls

4 calls:

25.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
23.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
21.0ms	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
21.0ms	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

series645.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
235.0ms	(log.f64 (cbrt.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
83.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
80.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5904	3456

prune276.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	164	4	168

Merged error: 0b

Counts

168 → 4

Compiler

Compiled 5454 to 3754 computations (31.2% saved)

regimes79.0ms (1.3%)

Compiler: Compiled 348 to 300 computations (13.8% saved)

bsearch135.0ms (2.2%)

Steps

Iters	Range		Point
11	8752128.221745025	5.203747434783173e+28	43088487.23901788
9	-92455205081.44498	-168.4726375836771	-48019698.52435404

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	171	103
1	171	103

end0.0ms (0%)

sample1.3s (21.6%)

Algorithm

1×

intervals

Results

305.0ms	5805×	body	128	valid
202.0ms	1048×	body	1024	valid
154.0ms	1027×	body	1024	nan
89.0ms	672×	body	512	valid
73.0ms	681×	body	512	nan
35.0ms	397×	body	256	valid
26.0ms	364×	body	256	nan
23.0ms	78×	body	2048	valid
19.0ms	507×	body	128	nan
1.0ms	3×	body	2048	nan

Compiler

Compiled 211 to 161 computations (23.7% saved)

Details

analyze532.0ms (8.5%)

sample35.0ms (0.6%)

simplify343.0ms (5.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite96.0ms (1.5%)

series364.0ms (5.8%)

simplify85.0ms (1.4%)

prune702.0ms (11.3%)

localize13.0ms (0.2%)

rewrite23.0ms (0.4%)

series249.0ms (4%)

simplify73.0ms (1.2%)

prune101.0ms (1.6%)

localize10.0ms (0.2%)

rewrite105.0ms (1.7%)

series406.0ms (6.5%)

simplify96.0ms (1.5%)

prune298.0ms (4.8%)

localize12.0ms (0.2%)

rewrite111.0ms (1.8%)

series645.0ms (10.4%)

simplify84.0ms (1.3%)

prune276.0ms (4.4%)

regimes79.0ms (1.3%)

bsearch135.0ms (2.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.3s (21.6%)

Profiling