Details

analyze1.1s (12.3%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.7%	90.9%	6.4%	9
4.1%	86.4%	9.5%	10
4.4%	86.1%	9.5%	11
19.7%	65.3%	15%	12
21.9%	60.4%	17.7%	13
22.7%	59.6%	17.7%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample53.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	34×	body	1024	valid
13.0ms	192×	body	128	valid
6.0ms	23×	body	512	valid
3.0ms	7×	body	1024	invalid
2.0ms	45×	body	128	nan
1.0ms	5×	body	512	invalid
1.0ms	7×	body	256	valid
1.0ms	6×	body	256	invalid
1.0ms	11×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4929	16
1	4929	16

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 7.6b

Counts

2 → 1

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
0.0b	(/.f64 y (+.f64 y z))
7.2b	(pow.f64 (/.f64 y (+.f64 y z)) y)

rewrite76.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
81×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
8×	`add-cbrt-cube_binary64`
7×	`flip3-+_binary64` `associate-/r*_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `sqr-pow_binary64`
4×	`pow-exp_binary64`
3×	`pow-unpow_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 184

Calls

4 calls:

26.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
13.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
8.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
6.0ms	(/.f64 y (+.f64 y z))

series847.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
261.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
171.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
49.0ms	(/.f64 y (+.f64 y z))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4946	4340
1	4946	4340

prune316.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	5	196
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	5	197

Merged error: 0.8b

Counts

197 → 5

Compiler

Compiled 7289 to 2574 computations (64.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.9b	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
2.6b	(pow.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 y z)) (cbrt.f64 (+.f64 y z)))) y)

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`cbrt-prod_binary64`
61×	`unpow-prod-down_binary64`
55×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64` `times-frac_binary64`
22×	`add-exp-log_binary64`
14×	`cbrt-div_binary64`
13×	`pow1_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64` `pow-exp_binary64`
6×	`pow-unpow_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`prod-exp_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

18.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 y z)) (cbrt.f64 (+.f64 y z)))) y)
13.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

series1.3s (14.2%)

Counts

4 → 12

Calls

4 calls:

493.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 y z)) (cbrt.f64 (+.f64 y z)))) y)
446.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
193.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
157.0ms	(cbrt.f64 y)

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4901	3332
1	4901	3332

prune211.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	155	7	162

Merged error: 0b

Counts

162 → 7

Compiler

Compiled 6528 to 1513 computations (76.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.9b	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)
0.9b	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)
0.9b	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`unpow-prod-down_binary64`
49×	`*-un-lft-identity_binary64`
48×	`cbrt-prod_binary64`
42×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`pow-unpow_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`distribute-lft-out_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64`
2×	`cbrt-div_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 108

Calls

4 calls:

14.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
3.0ms	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)
3.0ms	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)
1.0ms	(cbrt.f64 y)

series772.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

440.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
161.0ms	(cbrt.f64 y)
91.0ms	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)
80.0ms	(pow.f64 (fabs.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z)))) y)

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4979	2890
1	4979	2890

prune146.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 0b

Counts

127 → 7

Compiler

Compiled 5341 to 853 computations (84% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.9b	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
0.9b	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
0.9b	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)

rewrite78.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`unpow-prod-down_binary64`
138×	`cbrt-prod_binary64`
126×	`times-frac_binary64`
125×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`distribute-lft-out_binary64`
13×	`add-exp-log_binary64`
9×	`pow-unpow_binary64`
7×	`pow1_binary64`
6×	`cbrt-div_binary64` `associate-/r/_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow1/3_binary64`

Counts

4 → 200

Calls

4 calls:

17.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
13.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
13.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
1.0ms	(cbrt.f64 y)

series1.5s (16.4%)

Counts

4 → 12

Calls

4 calls:

449.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
444.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
440.0ms	(pow.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y z))) y)
156.0ms	(cbrt.f64 y)

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4944	5806
1	4944	5806

prune247.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	212	7	219

Merged error: 0b

Counts

219 → 7

Compiler

Compiled 9119 to 1425 computations (84.4% saved)

regimes59.0ms (0.6%)

Compiler: Compiled 543 to 267 computations (50.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	43
1	22	43

end0.0ms (0%)

sample1.7s (18.9%)

Algorithm

1×

intervals

Results

419.0ms	6103×	body	128	valid
395.0ms	956×	body	1024	valid
153.0ms	610×	body	512	valid
70.0ms	181×	body	1024	invalid
54.0ms	228×	body	512	invalid
53.0ms	1072×	body	128	nan
50.0ms	329×	body	256	valid
29.0ms	437×	body	128	invalid
21.0ms	132×	body	256	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 249 to 133 computations (46.6% saved)

Details

analyze1.1s (12.3%)

sample53.0ms (0.6%)

simplify58.0ms (0.6%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

rewrite76.0ms (0.8%)

series847.0ms (9.3%)

simplify100.0ms (1.1%)

prune316.0ms (3.5%)

localize19.0ms (0.2%)

rewrite66.0ms (0.7%)

series1.3s (14.2%)

simplify114.0ms (1.3%)

prune211.0ms (2.3%)

localize18.0ms (0.2%)

rewrite37.0ms (0.4%)

series772.0ms (8.5%)

simplify115.0ms (1.3%)

prune146.0ms (1.6%)

localize15.0ms (0.2%)

rewrite78.0ms (0.9%)

series1.5s (16.4%)

simplify102.0ms (1.1%)

prune247.0ms (2.7%)

regimes59.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (18.9%)

Profiling