Details

analyze419.0ms (3.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
49.9%	49.9%	0.3%	5
49.9%	49.9%	0.3%	6
49.9%	49.9%	0.3%	7
49.9%	49.9%	0.3%	8
49.9%	49.9%	0.3%	9
49.9%	49.9%	0.3%	10
49.9%	24.9%	25.2%	11
49.9%	24.9%	25.2%	12
49.9%	24.9%	25.2%	13
49.9%	24.9%	25.2%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.7s (15%)

Infinites

13.5% of outputs are infinite.

Symmetry

(sort x y)

Results

1.1s	8252×	body	128	valid
500.0ms	4055×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify281.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

5327×	`fma-def_binary64`
866×	`fma-neg_binary64`
705×	`sub-neg_binary64`
654×	`unsub-neg_binary64`
445×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	35	22
2	101	22
3	269	21
4	805	20
5	2079	20
6	2787	20
7	3848	20
8	4164	20
9	4306	20
10	4090	20
11	4094	20
12	4190	20
13	4488	20
14	4581	20
15	4587	20
16	4587	20
17	4593	20
18	4599	20
19	4599	20
20	4617	20
21	4601	20
22	4601	20
23	9364	20

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 120 to 79 computations (34.2% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series217.0ms (2%)

Counts

2 → 120

Calls

2 calls:

208.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
9.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
0.0ms	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

688×	`associate--l+_binary64`
559×	`exp-diff_binary64`
446×	`associate-+l-_binary64`
320×	`associate-l_binary64`
296×	`associate-r_binary64`

Counts

140 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	2481
1	211	2304
2	554	2131
3	2029	2131
4	4532	2131
5	5214	2131

prune61.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Error

0.0b

Counts

69 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
	32.2b	(*.f64 (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (sqrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
	1.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y))))) (cbrt.f64 (fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))))
	13.1b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 1403 to 736 computations (47.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series546.0ms (4.9%)

Counts

4 → 140

Calls

4 calls:

212.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
204.0ms	(*.f64 z (log.f64 t))
126.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
4.0ms	(*.f64 (-.f64 a 1/2) b)

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
27×	`add-log-exp_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`

Counts

4 → 116

Calls

4 calls:

9.0ms	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t))) (.f64 (-.f64 a 1/2) b))
8.0ms	(-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))
4.0ms	(*.f64 (-.f64 a 1/2) b)
3.0ms	(*.f64 z (log.f64 t))

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

395×	`associate--l+_binary64`
356×	`fma-neg_binary64`
311×	`exp-sum_binary64`
252×	`cancel-sign-sub-inv_binary64`
193×	`associate--r+_binary64`

Counts

256 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	4510
1	661	4261
2	2495	4222
3	4593	4222
4	5122	4222

prune199.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	203	5	208
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	207	6	213

Error

0.0b

Counts

213 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	0.3b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 (.f64 (cbrt.f64 (.f64 z (log.f64 t))) (cbrt.f64 (.f64 z (log.f64 t)))) (cbrt.f64 (.f64 z (log.f64 t))))) (.f64 (-.f64 a 1/2) b))
	31.9b	(fma.f64 (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (*.f64 (-.f64 a 1/2) b))
	12.3b	(-.f64 (fma.f64 b a (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 b 1/2)))
	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (.f64 (log.f64 (cbrt.f64 t)) z)) (.f64 (-.f64 a 1/2) b))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 5399 to 1958 computations (63.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 z (log.f64 (cbrt.f64 t)))
✓	0.3b	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
✓	0.3b	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
✓	0.6b	(cbrt.f64 t)

series3.6s (32.8%)

Counts

4 → 84

Calls

4 calls:

1.4s	(*.f64 z (log.f64 (cbrt.f64 t)))
1.2s	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
1.1s	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
30.0ms	(cbrt.f64 t)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`log-prod_binary64`
60×	`distribute-lft-in_binary64`
60×	`distribute-rgt-in_binary64`
39×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

4 → 142

Calls

4 calls:

7.0ms	(+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 z (log.f64 (cbrt.f64 t))))
5.0ms	(*.f64 z (log.f64 (cbrt.f64 t)))
5.0ms	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
1.0ms	(cbrt.f64 t)

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
475×	`fma-neg_binary64`
441×	`*-commutative_binary64`
440×	`cancel-sign-sub-inv_binary64`
306×	`distribute-rgt-in_binary64`

Counts

226 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3066
1	407	2725
2	1353	2500
3	3821	2492
4	4971	2492

prune298.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	248	6	254

Error

Counts

254 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 3 (.f64 (log.f64 (pow.f64 t 1/3)) z))) (*.f64 (-.f64 a 1/2) b))
	31.9b	(fma.f64 (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (*.f64 (-.f64 a 1/2) b))
	12.3b	(-.f64 (fma.f64 b a (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 b 1/2)))
▶	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (.f64 (log.f64 (cbrt.f64 t)) z)) (.f64 (-.f64 a 1/2) b))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 7964 to 3233 computations (59.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z))
✓	0.3b	(*.f64 (log.f64 (cbrt.f64 t)) z)
	0.3b	(.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))
	0.6b	(cbrt.f64 t)

series1.9s (17.5%)

Counts

2 → 72

Calls

2 calls:

1.1s	(*.f64 (log.f64 (cbrt.f64 t)) z)
863.0ms	(-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64`
12×	`*-un-lft-identity_binary64`
9×	`associate--l+_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`prod-diff_binary64`

Counts

2 → 54

Calls

2 calls:

11.0ms	(-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (*.f64 (log.f64 (cbrt.f64 t)) z))
3.0ms	(*.f64 (log.f64 (cbrt.f64 t)) z)

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-neg_binary64`
451×	`fma-def_binary64`
320×	`distribute-rgt-in_binary64`
314×	`distribute-lft-in_binary64`
272×	`cancel-sign-sub-inv_binary64`

Counts

126 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	2305
1	326	1926
2	1015	1679
3	3730	1669
4	4849	1669

prune211.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	193	6	199

Error

Counts

199 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (+.f64 (.f64 z (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 z (log.f64 (cbrt.f64 t))))) (.f64 (-.f64 a 1/2) b))
	0.1b	(+.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 3 (.f64 (log.f64 (pow.f64 t 1/3)) z))) (*.f64 (-.f64 a 1/2) b))
	31.9b	(fma.f64 (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (sqrt.f64 (-.f64 (+.f64 (+.f64 x y) z) (.f64 z (log.f64 t)))) (*.f64 (-.f64 a 1/2) b))
	12.3b	(-.f64 (fma.f64 b a (+.f64 z x)) (fma.f64 z (log.f64 t) (*.f64 b 1/2)))
✓	0.1b	(+.f64 (-.f64 (-.f64 (+.f64 y (+.f64 z x)) (.f64 z (.f64 2 (log.f64 (cbrt.f64 t))))) (.f64 (log.f64 (cbrt.f64 t)) z)) (.f64 (-.f64 a 1/2) b))
✓	0.1b	(fma.f64 z (-.f64 1 (log.f64 t)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))

Compiler

Compiled 6093 to 2577 computations (57.7% saved)

regimes911.0ms (8.2%)

Accuracy

Total 0.1b remaining (89.8%)

Threshold costs 0.1b (89.8%)

Counts

70 → 1

Compiler

Compiled 20105 to 13678 computations (32% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`*-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	40
1	37	40
2	47	40
3	66	40
4	84	40
5	94	40
6	99	40
7	100	40
8	98	40

end122.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 290 to 194 computations (33.1% saved)

Details

analyze419.0ms (3.8%)

sample1.7s (15%)

simplify281.0ms (2.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series217.0ms (2%)

rewrite2.0ms (0%)

simplify98.0ms (0.9%)

prune61.0ms (0.6%)

localize13.0ms (0.1%)

series546.0ms (4.9%)

rewrite33.0ms (0.3%)

simplify133.0ms (1.2%)

prune199.0ms (1.8%)

localize16.0ms (0.1%)

series3.6s (32.8%)

rewrite27.0ms (0.2%)

simplify127.0ms (1.1%)

prune298.0ms (2.7%)

localize18.0ms (0.2%)

series1.9s (17.5%)

rewrite17.0ms (0.2%)

simplify80.0ms (0.7%)

prune211.0ms (1.9%)

regimes911.0ms (8.2%)

simplify6.0ms (0.1%)

end122.0ms (1.1%)

Profiling