Details

analyze236.0ms (1.9%)

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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
49.9%	25%	25.1%	7
49.9%	25%	25.1%	8
49.9%	25%	25.1%	9
49.9%	12.5%	37.6%	10
49.9%	12.5%	37.6%	11
49.9%	12.5%	37.6%	12
49.9%	6.2%	43.8%	13
49.9%	6.2%	43.8%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample2.0s (16.3%)

Results

1.5s	8256×	body	128	valid
171.0ms	1065×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify426.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

990×	`fma-def_binary64`
806×	`fma-neg_binary64`
746×	`unsub-neg_binary64`
520×	`distribute-rgt-in_binary64`
485×	`distribute-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	59	16
3	115	16
4	270	14
5	514	14
6	792	14
7	1191	14
8	1435	14
9	1716	14
10	2343	14
11	2639	14
12	2704	14
13	3251	14
14	3766	14
15	3977	14
16	4124	14
17	4234	14
18	4260	14
19	4085	14
20	4111	14
21	4149	14
22	4189	14
23	4189	14
24	4189	14
25	4871	14
26	4999	14
27	4907	14

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
✓	0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
✓	0.1b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

series576.0ms (4.6%)

Counts

3 → 72

Calls

3 calls:

420.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
146.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
9.0ms	(+.f64 (-.f64 1 z) (log.f64 z))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`
9×	`prod-diff_binary64`

Counts

3 → 85

Calls

3 calls:

14.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
12.0ms	(+.f64 (-.f64 1 z) (log.f64 z))
8.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

simplify212.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

353×	`times-frac_binary64`
345×	`associate-+l+_binary64`
335×	`*-commutative_binary64`
284×	`cancel-sign-sub-inv_binary64`
270×	`associate-+r+_binary64`

Counts

157 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2280
1	446	2015
2	1697	1951
3	3681	1950
4	4939	1950
5	4823	1950

prune184.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	8	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Error

0.0b

Counts

150 → 8

Alt Table

Status	Error	Program
	30.6b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))))
▶	0.1b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z)))))
	33.7b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	13.5b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
	24.7b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (+.f64 (pow.f64 (-.f64 1 z) 3) (pow.f64 (log.f64 z) 3))) (+.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (-.f64 (.f64 (log.f64 z) (log.f64 z)) (*.f64 (-.f64 1 z) (log.f64 z))))))
	0.2b	(+.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 3243 to 1912 computations (41% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 1 z))
✓	0.0b	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
✓	0.1b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
✓	0.3b	(*.f64 (log.f64 (/.f64 1 z)) y)

series1.1s (9%)

Counts

4 → 52

Calls

4 calls:

506.0ms	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
365.0ms	(*.f64 (log.f64 (/.f64 1 z)) y)
218.0ms	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
34.0ms	(log.f64 (/.f64 1 z))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`log-prod_binary64`

Counts

4 → 108

Calls

4 calls:

16.0ms	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
8.0ms	(+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (.f64 y z))
7.0ms	(*.f64 (log.f64 (/.f64 1 z)) y)
4.0ms	(log.f64 (/.f64 1 z))

simplify357.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
410×	`cancel-sign-sub-inv_binary64`
256×	`distribute-rgt-neg-in_binary64`
252×	`distribute-rgt-neg-out_binary64`
251×	`distribute-lft-neg-out_binary64`

Counts

160 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3068
1	557	2494
2	2311	2283
3	4419	2283
4	4999	2283
5	4924	2283

prune340.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	178	9	187

Error

0.0b

Counts

187 → 9

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z)))))
	33.6b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (.f64 (neg.f64 (log.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)) (.f64 y z)))
	30.6b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))))
✓	0.1b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (log.f64 (/.f64 1 z)) y) (*.f64 y z)))
	33.7b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	13.5b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 y (-.f64 (.f64 (-.f64 1 z) (-.f64 1 z)) (.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
	0.3b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (/.f64 1 z))) (cbrt.f64 (log.f64 (/.f64 1 z)))) (.f64 y (cbrt.f64 (neg.f64 (log.f64 z))))) (*.f64 y z)))
▶	0.2b	(+.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 5275 to 2906 computations (44.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
✓	0.1b	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
✓	0.1b	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
✓	0.6b	(cbrt.f64 z)

series1.4s (11.3%)

Counts

4 → 60

Calls

4 calls:

985.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
206.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
188.0ms	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
41.0ms	(cbrt.f64 z)

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-log-exp_binary64`
14×	`associate-+l+_binary64`

Counts

4 → 101

Calls

4 calls:

12.0ms	(.f64 y (+.f64 (+.f64 (-.f64 1 z) (.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z))))
12.0ms	(+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2))
8.0ms	(+.f64 (+.f64 (-.f64 1 z) (*.f64 (log.f64 (cbrt.f64 z)) 2)) (log.f64 (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)

simplify261.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-+l+_binary64`
387×	`*-commutative_binary64`
334×	`fma-neg_binary64`
315×	`associate-+r+_binary64`
285×	`times-frac_binary64`

Counts

161 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2833
1	483	1965
2	1763	1828
3	3854	1826
4	4934	1826
5	4981	1826
6	4823	1826

prune483.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	197	3	200
Fresh	3	4	7
Picked	1	0	1
Done	1	0	1
Total	202	7	209

Error

0.0b

Counts

209 → 7

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z)))))
	33.6b	(-.f64 (+.f64 y (.f64 1/2 x)) (+.f64 (.f64 (.f64 (neg.f64 (log.f64 z)) (sqrt.f64 y)) (sqrt.f64 y)) (.f64 y z)))
	33.7b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 1 (*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (*.f64 (log.f64 (cbrt.f64 z)) y)))
	0.2b	(+.f64 (.f64 x 1/2) (-.f64 (+.f64 y (.f64 3 (.f64 y (log.f64 (pow.f64 z 1/3))))) (.f64 y z)))

Compiler

Compiled 5299 to 2977 computations (43.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (log.f64 z))
✓	0.0b	(+.f64 (.f64 x 1/2) (.f64 1 (*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)))
✓	0.0b	(-.f64 (+.f64 1 (log.f64 z)) z)
✓	0.1b	(*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)

series584.0ms (4.7%)

Counts

4 → 84

Calls

4 calls:

391.0ms	(*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)
148.0ms	(+.f64 (.f64 x 1/2) (.f64 1 (*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)))
32.0ms	(+.f64 1 (log.f64 z))
12.0ms	(-.f64 (+.f64 1 (log.f64 z)) z)

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`
14×	`distribute-lft-out_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)
11.0ms	(-.f64 (+.f64 1 (log.f64 z)) z)
8.0ms	(+.f64 (.f64 x 1/2) (.f64 1 (*.f64 (-.f64 (+.f64 1 (log.f64 z)) z) y)))
6.0ms	(+.f64 1 (log.f64 z))

simplify214.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1014×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
311×	`*-commutative_binary64`
250×	`times-frac_binary64`
223×	`associate-+l+_binary64`

Counts

187 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2482
1	463	2268
2	1542	2216
3	3291	2216
4	4960	2216
5	4904	2216

prune358.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Error

0.0b

Counts

167 → 6

Alt Table

Status	Error	Program
	13.5b	(+.f64 (.f64 x 1/2) (.f64 1 (/.f64 (.f64 (-.f64 (.f64 (+.f64 1 (log.f64 z)) (+.f64 1 (log.f64 z))) (*.f64 z z)) y) (+.f64 (+.f64 1 (log.f64 z)) z))))
	0.2b	(+.f64 (.f64 x 1/2) (-.f64 (+.f64 y (.f64 3 (.f64 y (log.f64 (pow.f64 z 1/3))))) (.f64 y z)))
	0.7b	(+.f64 (.f64 x 1/2) (.f64 (.f64 y (.f64 (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z))))) (cbrt.f64 (+.f64 (-.f64 1 z) (log.f64 z)))))
	33.7b	(+.f64 (.f64 x 1/2) (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z)))))
	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 (fma.f64 (log.f64 (cbrt.f64 z)) 2 1) z)) (*.f64 (log.f64 (cbrt.f64 z)) y)))
	25.2b	(+.f64 (.f64 x 1/2) (.f64 1 (.f64 (log.f64 (/.f64 (.f64 (exp.f64 1) z) (exp.f64 z))) y)))

Compiler

Compiled 3562 to 2179 computations (38.8% saved)

regimes3.3s (26.2%)

Accuracy

Total 0.1b remaining (87.2%)

Threshold costs 0.1b (87.2%)

Counts

201 → 1

Compiler

Compiled 30128 to 21847 computations (27.5% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	21	16
3	23	16
4	24	16
5	23	16

end177.0ms (1.4%)

Compiler: Compiled 173 to 121 computations (30.1% saved)

Details

analyze236.0ms (1.9%)

sample2.0s (16.3%)

simplify426.0ms (3.4%)

prune6.0ms (0%)

localize15.0ms (0.1%)

series576.0ms (4.6%)

rewrite40.0ms (0.3%)

simplify212.0ms (1.7%)

prune184.0ms (1.5%)

localize20.0ms (0.2%)

series1.1s (9%)

rewrite49.0ms (0.4%)

simplify357.0ms (2.8%)

prune340.0ms (2.7%)

localize13.0ms (0.1%)

series1.4s (11.3%)

rewrite43.0ms (0.3%)

simplify261.0ms (2.1%)

prune483.0ms (3.8%)

localize21.0ms (0.2%)

series584.0ms (4.7%)

rewrite51.0ms (0.4%)

simplify214.0ms (1.7%)

prune358.0ms (2.9%)

regimes3.3s (26.2%)

simplify6.0ms (0%)

end177.0ms (1.4%)

Profiling