Details

analyze400.0ms (7%)

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%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify513.0ms (9%)

Algorithm

1×	egg-herbie

Rules

2079×	`associate--r-_binary64`
910×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`
410×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	28	18
2	53	18
3	97	18
4	218	18
5	349	18
6	484	18
7	750	18
8	745	18
9	847	18
10	1341	18
11	1637	18
12	1702	18
13	2249	18
14	2764	18
15	2975	18
16	3122	18
17	3232	18
18	3258	18
19	3083	18
20	3109	18
21	3147	18
22	3187	18
23	3187	18
24	3187	18
25	3869	18
26	3679	18
27	3813	18
28	3759	18
29	3787	18
30	3793	18
31	3937	18
32	3913	18
33	3913	18
34	3913	18
35	3925	18
36	3917	18
37	6053	18

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
0.2b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

rewrite102.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

23×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64`
8×	`add-log-exp_binary64`

Counts

3 → 63

Calls

3 calls:

11.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
8.0ms	(+.f64 (-.f64 1 z) (log.f64 z))
6.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 1094 to 665 computations (39.2% saved)

series115.0ms (2%)

Error

0.1b

Counts

3 → 30

Calls

3 calls:

55.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
27.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
12.0ms	(+.f64 (-.f64 1 z) (log.f64 z))

Compiler

Compiled 931 to 611 computations (34.4% saved)

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

628×	`times-frac_binary64`
274×	`*-commutative_binary64`
273×	`associate-+l+_binary64`
265×	`sub-neg_binary64`
228×	`exp-sum_binary64`

Counts

93 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1360
1	365	1266
2	1271	1265
3	2678	1265
4	4345	1265
5	5422	1265

prune63.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Error

0.0b

Counts

71 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (.f64 1/2 x) (-.f64 y (.f64 z y))) (*.f64 (log.f64 z) y))
	32.3b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (-.f64 (+.f64 (log.f64 z) 1) z) (sqrt.f64 y))))
	29.2b	(/.f64 (+.f64 (.f64 x (.f64 x 1/4)) (.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (.f64 y (+.f64 -1 (-.f64 z (log.f64 z)))))) (+.f64 (.f64 1/2 x) (*.f64 y (+.f64 -1 (-.f64 z (log.f64 z))))))
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 1 (-.f64 (log.f64 z) z))))
	36.1b	(.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (.f64 1/2 x))) (sqrt.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (*.f64 1/2 x))))
	41.6b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (.f64 1/2 x)) 3))
	16.3b	(+.f64 (.f64 x 1/2) (.f64 y (/.f64 (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3)) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (.f64 (-.f64 1 z) (-.f64 (-.f64 1 z) (log.f64 z)))))))
	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))))

Compiler

Compiled 1129 to 709 computations (37.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 1 (-.f64 (log.f64 z) z))))
0.0b	(+.f64 1 (-.f64 (log.f64 z) z))
0.0b	(-.f64 (log.f64 z) z)
0.2b	(*.f64 y (+.f64 1 (-.f64 (log.f64 z) z)))

rewrite135.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

27×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
10×	`add-cube-cbrt_binary64`
9×	`associate-+r+_binary64`

Counts

4 → 81

Calls

4 calls:

9.0ms	(*.f64 y (+.f64 1 (-.f64 (log.f64 z) z)))
7.0ms	(+.f64 1 (-.f64 (log.f64 z) z))
5.0ms	(-.f64 (log.f64 z) z)
4.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 1 (-.f64 (log.f64 z) z))))

Compiler

Compiled 1423 to 739 computations (48.1% saved)

series130.0ms (2.3%)

Error

0.0b

Counts

4 → 35

Calls

4 calls:

58.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 1 (-.f64 (log.f64 z) z))))
26.0ms	(*.f64 y (+.f64 1 (-.f64 (log.f64 z) z)))
13.0ms	(-.f64 (log.f64 z) z)
11.0ms	(+.f64 1 (-.f64 (log.f64 z) z))

Compiler

Compiled 1106 to 741 computations (33% saved)

simplify121.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

375×	`unsub-neg_binary64`
284×	`times-frac_binary64`
276×	`sub-neg_binary64`
250×	`*-commutative_binary64`
243×	`associate-+l+_binary64`

Counts

116 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1509
1	396	1420
2	1196	1418
3	2635	1418
4	4255	1418
5	4956	1418

prune79.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	83	7	90

Error

Counts

90 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
	19.0b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 1 (pow.f64 (-.f64 (log.f64 z) z) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (*.f64 1 (-.f64 (log.f64 z) z))))))
	32.3b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (-.f64 (+.f64 (log.f64 z) 1) z) (sqrt.f64 y))))
	36.1b	(.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (.f64 1/2 x))) (sqrt.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (*.f64 1/2 x))))
	41.6b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (-.f64 (+.f64 (log.f64 z) 1) z) y) (.f64 1/2 x)) 3))
	16.3b	(+.f64 (.f64 x 1/2) (.f64 y (/.f64 (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3)) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (.f64 (-.f64 1 z) (-.f64 (-.f64 1 z) (log.f64 z)))))))
	15.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 1 (*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z))))

Compiler

Compiled 1329 to 793 computations (40.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 z) z)
0.1b	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
0.2b	(*.f64 (-.f64 (log.f64 z) z) y)

rewrite89.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

3 → 60

Calls

3 calls:

7.0ms	(*.f64 (-.f64 (log.f64 z) z) y)
6.0ms	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
4.0ms	(-.f64 (log.f64 z) z)

Compiler

Compiled 1280 to 518 computations (59.5% saved)

series111.0ms (2%)

Error

Counts

3 → 30

Calls

3 calls:

56.0ms	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
26.0ms	(*.f64 (-.f64 (log.f64 z) z) y)
11.0ms	(-.f64 (log.f64 z) z)

Compiler

Compiled 949 to 606 computations (36.1% saved)

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

661×	`unsub-neg_binary64`
374×	`*-commutative_binary64`
321×	`associate-+l+_binary64`
286×	`neg-sub0_binary64`
284×	`neg-mul-1_binary64`

Counts

90 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1538
1	455	1462
2	1483	1440
3	3461	1440
4	4863	1440

prune65.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	59	7	66

Error

Counts

66 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
	19.0b	(+.f64 (+.f64 y (.f64 1/2 x)) (/.f64 (.f64 y (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3))) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (+.f64 (.f64 z z) (*.f64 (log.f64 z) z)))))
	27.9b	(*.f64 y (+.f64 1 (-.f64 (log.f64 z) z)))
	19.0b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 1 (pow.f64 (-.f64 (log.f64 z) z) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)) (*.f64 1 (-.f64 (log.f64 z) z))))))
	26.7b	(+.f64 (+.f64 y (.f64 1/2 x)) (cbrt.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3)))
	16.3b	(+.f64 (.f64 x 1/2) (.f64 y (/.f64 (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3)) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (.f64 (-.f64 1 z) (-.f64 (-.f64 1 z) (log.f64 z)))))))
▶	15.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 1 (*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z))))

Compiler

Compiled 1184 to 573 computations (51.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (log.f64 z) z)
0.3b	(*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))
5.1b	(.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))))
9.5b	(/.f64 (.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z)))

rewrite228.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
28×	`distribute-lft-out--_binary64`
24×	`pow1_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 143

Calls

4 calls:

13.0ms	(/.f64 (.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z)))
12.0ms	(*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))
7.0ms	(.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))))
5.0ms	(-.f64 (log.f64 z) z)

Compiler

Compiled 4124 to 1563 computations (62.1% saved)

series230.0ms (4%)

Error

Counts

4 → 30

Calls

4 calls:

83.0ms	(/.f64 (.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z)))
76.0ms	(.f64 y (-.f64 1 (.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))))
22.0ms	(*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z))
12.0ms	(-.f64 (log.f64 z) z)

Compiler

Compiled 2102 to 1398 computations (33.5% saved)

simplify164.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

295×	`associate-/l/_binary64`
239×	`cancel-sign-sub-inv_binary64`
199×	`associate-l_binary64`
194×	`associate-r_binary64`
186×	`distribute-rgt-neg-out_binary64`

Counts

173 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	4002
1	662	3577
2	2458	3288
3	4597	3121
4	4962	3121

prune132.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	142	7	149

Error

Counts

149 → 7

Alt Table

Status	Error	Program
	15.3b	(+.f64 (.f64 x 1/2) (/.f64 1 (/.f64 (-.f64 (+.f64 z 1) (log.f64 z)) (.f64 y (-.f64 1 (pow.f64 (-.f64 (log.f64 z) z) 2))))))
	12.2b	(+.f64 (.f64 x 1/2) (.f64 y (/.f64 (-.f64 1 (pow.f64 (-.f64 (log.f64 z) z) 2)) (-.f64 (+.f64 z 1) (log.f64 z)))))
	0.1b	(+.f64 (+.f64 y (.f64 1/2 x)) (.f64 (-.f64 (log.f64 z) z) y))
	19.0b	(+.f64 (+.f64 y (.f64 1/2 x)) (/.f64 (.f64 y (-.f64 (pow.f64 (log.f64 z) 3) (pow.f64 z 3))) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (+.f64 (.f64 z z) (*.f64 (log.f64 z) z)))))
	26.7b	(+.f64 (+.f64 y (.f64 1/2 x)) (cbrt.f64 (pow.f64 (.f64 y (-.f64 (log.f64 z) z)) 3)))
	16.3b	(+.f64 (.f64 x 1/2) (.f64 y (/.f64 (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3)) (+.f64 (.f64 (log.f64 z) (log.f64 z)) (.f64 (-.f64 1 z) (-.f64 (-.f64 1 z) (log.f64 z)))))))
	15.2b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 1 (*.f64 (-.f64 (log.f64 z) z) (-.f64 (log.f64 z) z)))) (-.f64 1 (-.f64 (log.f64 z) z))))

Compiler

Compiled 2551 to 1294 computations (49.3% saved)

regimes1.6s (28.9%)

Accuracy

Total 0.1b remaining (73.8%)

Threshold costs 0.1b (73.8%)

Compiler

Compiled 25761 to 16808 computations (34.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`mul-1-neg_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	24	18
2	26	18
3	27	18
4	28	18
5	26	18

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample1.1s (19.3%)

Algorithm

1×

intervals

Results

610.0ms	8000×	body	128	valid
14.0ms	305×	body	128	invalid
2.0ms	60×	body	128	nan

Compiler

Compiled 214 to 144 computations (32.7% saved)

Details

analyze400.0ms (7%)

sample23.0ms (0.4%)

simplify513.0ms (9%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite102.0ms (1.8%)

series115.0ms (2%)

simplify107.0ms (1.9%)

prune63.0ms (1.1%)

localize10.0ms (0.2%)

rewrite135.0ms (2.4%)

series130.0ms (2.3%)

simplify121.0ms (2.1%)

prune79.0ms (1.4%)

localize9.0ms (0.2%)

rewrite89.0ms (1.6%)

series111.0ms (2%)

simplify89.0ms (1.6%)

prune65.0ms (1.1%)

localize14.0ms (0.2%)

rewrite228.0ms (4%)

series230.0ms (4%)

simplify164.0ms (2.9%)

prune132.0ms (2.3%)

regimes1.6s (28.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (19.3%)

Profiling