Details

analyze762.0ms (5.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5331	64
0	3	3
1	3	3

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
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Symmetry

(sort x y)

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample30.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
2.0ms	66×	body	128	invalid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5346	16

prune3.0ms (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

Error

16.8b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (.f64 z z) (+.f64 z 1))
16.3b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

rewrite82.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

28×	`add-exp-log_binary64_9323` `add-cbrt-cube_binary64_9321`
12×	`prod-exp_binary64_9334` `cbrt-unprod_binary64_9318`
7×	`pow1_binary64_9346`
6×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
5×	`*-un-lft-identity_binary64_9285`
4×	`add-sqr-sqrt_binary64_9307` `associate-r/_binary64_9227` `associate-r*_binary64_9225`
3×	`add-cube-cbrt_binary64_9320` `pow-prod-down_binary64_9356`
2×	`add-log-exp_binary64_9324` `flip3-+_binary64_9288` `associate-/r/_binary64_9231` `flip-+_binary64_9259`
1×	`frac-2neg_binary64_9296` `times-frac_binary64_9291` `clear-num_binary64_9284` `div-inv_binary64_9282` `associate-/l_binary64_9230` `associate-/r_binary64_9229` `unswap-sqr_binary64_9253` `distribute-rgt-in_binary64_9235` `distribute-lft-in_binary64_9234` `associate-l_binary64_9226` `distribute-lft-out_binary64_9236` `*-commutative_binary64_9216`

Counts

2 → 51

Calls

2 calls:

10.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
8.0ms	(.f64 (.f64 z z) (+.f64 z 1))

Compiler

Compiled 1000 to 448 computations (55.2% saved)

series274.0ms (2%)

Error

16.8b

Counts

2 → 24

Calls

2 calls:

214.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
39.0ms	(.f64 (.f64 z z) (+.f64 z 1))

Compiler

Compiled 763 to 504 computations (33.9% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4961	1149
1	4961	1149

prune70.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Error

4.2b

Counts

76 → 9

Compiler

Compiled 1191 to 580 computations (51.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
4.6b	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
8.6b	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))

rewrite283.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

243×	`times-frac_binary64_9291`
132×	`*-un-lft-identity_binary64_9285`
88×	`add-cube-cbrt_binary64_9320` `add-sqr-sqrt_binary64_9307`
45×	`associate-/r*_binary64_9229`
35×	`add-exp-log_binary64_9323` `add-cbrt-cube_binary64_9321`
22×	`distribute-lft-out_binary64_9236`
20×	`associate-/r/_binary64_9231`
18×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
13×	`div-inv_binary64_9282`
7×	`flip3-+_binary64_9288` `flip-+_binary64_9259` `associate-/l*_binary64_9230`
4×	`prod-exp_binary64_9334` `cbrt-unprod_binary64_9318`
3×	`pow1_binary64_9346` `add-log-exp_binary64_9324` `frac-2neg_binary64_9296` `clear-num_binary64_9284`

Counts

3 → 205

Calls

3 calls:

13.0ms	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))
13.0ms	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
6.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 4356 to 2315 computations (46.9% saved)

series415.0ms (3%)

Error

4.2b

Counts

3 → 42

Calls

3 calls:

210.0ms	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))
110.0ms	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
64.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 1383 to 902 computations (34.8% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5049	5043

prune233.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	238	9	247
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	245	11	256

Error

0.0b

Counts

256 → 11

Compiler

Compiled 4557 to 2201 computations (51.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 z (.f64 (cbrt.f64 (/.f64 y (+.f64 z 1))) (cbrt.f64 (/.f64 y (+.f64 z 1))))))
8.0b	(cbrt.f64 (/.f64 y (+.f64 z 1)))
8.0b	(cbrt.f64 (/.f64 y (+.f64 z 1)))
8.0b	(cbrt.f64 (/.f64 y (+.f64 z 1)))

rewrite273.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`cbrt-prod_binary64_9316`
52×	`times-frac_binary64_9291`
50×	`*-un-lft-identity_binary64_9285`
32×	`add-cube-cbrt_binary64_9320` `add-sqr-sqrt_binary64_9307`
25×	`add-exp-log_binary64_9323`
15×	`add-cbrt-cube_binary64_9321`
13×	`associate-/r/_binary64_9231`
11×	`cbrt-div_binary64_9317`
10×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `associate-/r*_binary64_9229`
9×	`distribute-lft-out_binary64_9236`
6×	`div-inv_binary64_9282`
5×	`prod-exp_binary64_9334` `cbrt-unprod_binary64_9318`
4×	`pow1_binary64_9346` `add-log-exp_binary64_9324`
3×	`pow1/3_binary64_9367` `flip3-+_binary64_9288` `flip-+_binary64_9259`
2×	`frac-times_binary64_9295` `associate-l/_binary64_9228` `associate-r/_binary64_9227`
1×	`frac-2neg_binary64_9296` `clear-num_binary64_9284` `associate-/l*_binary64_9230`

Counts

4 → 125

Calls

4 calls:

20.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 z (.f64 (cbrt.f64 (/.f64 y (+.f64 z 1))) (cbrt.f64 (/.f64 y (+.f64 z 1))))))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))

Compiler

Compiled 5303 to 3044 computations (42.6% saved)

series1.4s (9.8%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

627.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 z (.f64 (cbrt.f64 (/.f64 y (+.f64 z 1))) (cbrt.f64 (/.f64 y (+.f64 z 1))))))
217.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
212.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
201.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))

Compiler

Compiled 6085 to 4479 computations (26.4% saved)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	4292
1	4954	4292

prune349.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	177	12	189

Error

Counts

189 → 12

Compiler

Compiled 7241 to 4303 computations (40.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (/.f64 y (+.f64 z 1)))))
8.0b	(cbrt.f64 (/.f64 y (+.f64 1 z)))
8.0b	(cbrt.f64 (/.f64 y (+.f64 1 z)))
8.0b	(cbrt.f64 (/.f64 y (+.f64 z 1)))

rewrite2.0s (14%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1137×	`times-frac_binary64_9291`
653×	`*-un-lft-identity_binary64_9285`
639×	`cbrt-prod_binary64_9316`
509×	`add-cube-cbrt_binary64_9320` `add-sqr-sqrt_binary64_9307`
72×	`distribute-lft-out_binary64_9236`
68×	`associate-/r*_binary64_9229`
56×	`associate-/r/_binary64_9231`
32×	`div-inv_binary64_9282`
24×	`flip3-+_binary64_9288` `flip-+_binary64_9259`
10×	`cbrt-div_binary64_9317`
9×	`add-exp-log_binary64_9323`
6×	`add-cbrt-cube_binary64_9321` `associate-/l*_binary64_9230`
4×	`pow1_binary64_9346` `add-log-exp_binary64_9324`
3×	`pow1/3_binary64_9367` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
1×	`frac-2neg_binary64_9296` `clear-num_binary64_9284`

Counts

4 → 578

Calls

4 calls:

25.0ms	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (/.f64 y (+.f64 z 1)))))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 1 z)))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
5.0ms	(cbrt.f64 (/.f64 y (+.f64 1 z)))

Compiler

Compiled 28717 to 15458 computations (46.2% saved)

series1.2s (8.5%)

Error

Counts

4 → 55

Calls

4 calls:

466.0ms	(/.f64 (cbrt.f64 x) (/.f64 z (cbrt.f64 (/.f64 y (+.f64 z 1)))))
211.0ms	(cbrt.f64 (/.f64 y (+.f64 z 1)))
201.0ms	(cbrt.f64 (/.f64 y (+.f64 1 z)))
201.0ms	(cbrt.f64 (/.f64 y (+.f64 1 z)))

Compiler

Compiled 6347 to 4485 computations (29.3% saved)

simplify232.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

633 → 633

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5011	22776

prune2.0s (14%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	633	0	633
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	633	12	645

Error

Counts

645 → 12

Compiler

Compiled 29984 to 15967 computations (46.7% saved)

regimes1.5s (10.4%)

Accuracy

Total 1.1b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 15948 to 11838 computations (25.8% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	52
1	21	52

Remove

(sort x y)

Compiler

Compiled 66 to 46 computations (30.3% saved)

end0.0ms (0%)

sample2.7s (19.1%)

Algorithm

1×

intervals

Results

273.0ms	8000×	body	128	valid
56.0ms	1515×	body	128	invalid

Compiler

Compiled 2568 to 1907 computations (25.7% saved)

Details

analyze762.0ms (5.4%)

sample30.0ms (0.2%)

simplify93.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite82.0ms (0.6%)

series274.0ms (2%)

simplify68.0ms (0.5%)

prune70.0ms (0.5%)

localize7.0ms (0.1%)

rewrite283.0ms (2%)

series415.0ms (3%)

simplify93.0ms (0.7%)

prune233.0ms (1.7%)

localize16.0ms (0.1%)

rewrite273.0ms (1.9%)

series1.4s (9.8%)

simplify87.0ms (0.6%)

prune349.0ms (2.5%)

localize18.0ms (0.1%)

rewrite2.0s (14%)

series1.2s (8.5%)

simplify232.0ms (1.7%)

prune2.0s (14%)

regimes1.5s (10.4%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample2.7s (19.1%)

Profiling