Details

analyze1.2s (10.7%)

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
0%	74.8%	25.2%	5
0%	74.8%	25.2%	6
0%	74.8%	25.2%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	62.3%	37.7%	10
0%	56.1%	43.9%	11
0%	56.1%	43.9%	12
1.6%	54.5%	43.9%	13
2.4%	53.7%	43.9%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample122.0ms (1.1%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

27.0ms	256×	body	128	valid
3.0ms	43×	body	128	invalid
2.0ms	37×	body	128	nan

Compiler

Compiled 51 to 37 computations (27.5% saved)

simplify285.0ms (2.6%)

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

0.0b

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

series240.0ms (2.2%)

Counts

2 → 120

Calls

2 calls:

230.0ms	(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))

rewrite1.0ms (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))

simplify108.0ms (1%)

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

prune60.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.0b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	12.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))

Compiler

Compiled 1243 to 642 computations (48.4% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.2b	(*.f64 z (-.f64 1 (log.f64 t)))

series250.0ms (2.3%)

Counts

1 → 24

Calls

1 calls:

250.0ms

(*.f64 z (-.f64 1 (log.f64 t)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
17×	`distribute-lft-in_binary64`

Counts

1 → 60

Calls

1 calls:

7.0ms

(*.f64 z (-.f64 1 (log.f64 t)))

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
641×	`fma-neg_binary64`
476×	`associate-+l+_binary64`
455×	`associate-+r+_binary64`
302×	`distribute-rgt-neg-out_binary64`

Counts

84 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1157
1	172	1023
2	564	899
3	1294	824
4	3119	824
5	4632	824
6	4928	824
7	4745	824

prune83.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

Counts

96 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.0b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	0.8b	(+.f64 (/.f64 (.f64 z (-.f64 1 (pow.f64 (log.f64 t) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (log.f64 t) (log.f64 t)) (.f64 1 (log.f64 t))))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	12.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))

Compiler

Compiled 2496 to 1175 computations (52.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 a 1/2) b (+.f64 x y))
✓	0.2b	(-.f64 z (*.f64 z (log.f64 t)))
✓	0.2b	(*.f64 z (log.f64 t))

series699.0ms (6.5%)

Counts

2 → 28

Calls

2 calls:

474.0ms	(-.f64 z (*.f64 z (log.f64 t)))
225.0ms	(*.f64 z (log.f64 t))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
6×	`associate--r+_binary64`

Counts

2 → 53

Calls

2 calls:

6.0ms	(*.f64 z (log.f64 t))
3.0ms	(-.f64 z (*.f64 z (log.f64 t)))

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-neg_binary64`
355×	`unsub-neg_binary64`
270×	`fma-def_binary64`
267×	`times-frac_binary64`
252×	`sub-neg_binary64`

Counts

81 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	871
1	220	781
2	634	776
3	1730	774
4	3513	774
5	4916	774
6	4967	774
7	4791	774

prune114.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.0b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
▶	0.1b	(+.f64 (-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	12.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))

Compiler

Compiled 2396 to 944 computations (60.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)
✓	0.3b	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 (log.f64 (cbrt.f64 t)) z))
✓	0.3b	(*.f64 (log.f64 (cbrt.f64 t)) z)
✓	0.6b	(cbrt.f64 t)

series5.0s (46.2%)

Counts

4 → 84

Calls

4 calls:

2.4s	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 (log.f64 (cbrt.f64 t)) z))
1.4s	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)
1.2s	(*.f64 (log.f64 (cbrt.f64 t)) z)
32.0ms	(cbrt.f64 t)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 66

Calls

4 calls:

4.0ms	(*.f64 (log.f64 (cbrt.f64 t)) z)
3.0ms	(-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 (log.f64 (cbrt.f64 t)) z))
1.0ms	(cbrt.f64 t)
0.0ms	(fma.f64 z (*.f64 (log.f64 (cbrt.f64 t)) -2) z)

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-neg_binary64`
332×	`fma-def_binary64`
289×	`cancel-sign-sub-inv_binary64`
244×	`log-prod_binary64`
224×	`*-commutative_binary64`

Counts

150 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2097
1	306	1828
2	878	1548
3	2551	1543
4	4380	1543
5	4997	1543
6	4804	1543

prune133.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	133	4	137

Error

Counts

137 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 z (*.f64 z (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.0b	(+.f64 (*.f64 z (-.f64 1 (log.f64 t))) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
✓	0.1b	(+.f64 (-.f64 (fma.f64 z (.f64 (log.f64 (cbrt.f64 t)) -2) z) (.f64 (log.f64 (cbrt.f64 t)) z)) (fma.f64 (-.f64 a 1/2) b (+.f64 x y)))
	12.2b	(-.f64 (+.f64 (.f64 a b) (+.f64 y x)) (.f64 1/2 b))

Compiler

Compiled 3860 to 1677 computations (56.6% saved)

regimes764.0ms (7.1%)

Accuracy

Total 0.1b remaining (68.8%)

Threshold costs 0.1b (68.8%)

Counts

58 → 1

Compiler

Compiled 15565 to 10792 computations (30.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	26	22
2	31	22
3	33	22
4	34	22
5	32	22

end8.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 63 to 45 computations (28.6% saved)

sample1.4s (12.6%)

Algorithm

1×

intervals

Results

605.0ms	7997×	body	128	valid
88.0ms	1173×	body	128	invalid
72.0ms	1170×	body	128	nan
1.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 138 to 96 computations (30.4% saved)

Details

analyze1.2s (10.7%)

sample122.0ms (1.1%)

simplify285.0ms (2.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series240.0ms (2.2%)

rewrite1.0ms (0%)

simplify108.0ms (1%)

prune60.0ms (0.6%)

localize17.0ms (0.2%)

series250.0ms (2.3%)

rewrite11.0ms (0.1%)

simplify105.0ms (1%)

prune83.0ms (0.8%)

localize12.0ms (0.1%)

series699.0ms (6.5%)

rewrite11.0ms (0.1%)

simplify105.0ms (1%)

prune114.0ms (1.1%)

localize17.0ms (0.2%)

series5.0s (46.2%)

rewrite10.0ms (0.1%)

simplify117.0ms (1.1%)

prune133.0ms (1.2%)

regimes764.0ms (7.1%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample1.4s (12.6%)

Profiling