Details

analyze614.0ms (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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
49.9%	49.9%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
71.8%	28.1%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
85%	14.8%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample143.0ms (1.6%)

Algorithm

1×

intervals

Results

50.0ms	57×	body	1024	valid
30.0ms	14×	body	256	valid
26.0ms	154×	body	128	valid
15.0ms	31×	body	512	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 y)
✓	0.0b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series54.0ms (0.6%)

Counts

3 → 64

Calls

3 calls:

35.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
15.0ms	(*.f64 z (cos.f64 y))
4.0ms	(sin.f64 y)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

6.0ms	(*.f64 z (cos.f64 y))
2.0ms	(sin.f64 y)
1.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify174.0ms (2%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-neg_binary64`
413×	`sub-neg_binary64`
295×	`associate-l_binary64`
259×	`unswap-sqr_binary64`
258×	`associate-r_binary64`

Counts

103 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1076
1	225	1013
2	651	994
3	1798	994
4	3982	994
5	4885	994
6	5000	994
7	4925	994

prune118.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	6.7b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
	29.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	32.1b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))

Compiler

Compiled 1371 to 502 computations (63.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
✓	0.7b	(cbrt.f64 (sin.f64 y))

series759.0ms (8.7%)

Counts

3 → 36

Calls

3 calls:

427.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
327.0ms	(cbrt.f64 (sin.f64 y))
4.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y)))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y)))
10.0ms	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))
2.0ms	(cbrt.f64 (sin.f64 y))

simplify190.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-neg_binary64`
648×	`fma-def_binary64`
559×	`unswap-sqr_binary64`
438×	`log-prod_binary64`
348×	`sub-neg_binary64`

Counts

129 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	130	1271
1	296	1141
2	793	1085
3	1495	1035
4	3469	847
5	4207	847
6	4528	847
7	4911	847
8	4868	847

prune311.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	223	7	230

Error

0.0b

Counts

230 → 7

Alt Table

Status	Error	Program
	5.0b	(fma.f64 x (.f64 (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	29.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	32.1b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))

Compiler

Compiled 5065 to 1388 computations (72.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.4b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
✓	0.4b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series507.0ms (5.8%)

Counts

4 → 72

Calls

4 calls:

341.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
68.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
58.0ms	(cbrt.f64 z)
39.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
7.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
1.0ms	(cbrt.f64 z)

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
458×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1636
1	297	1460
2	1128	1401
3	2242	1385
4	4280	1287
5	4570	1287
6	4884	1287
7	4872	1287

prune146.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
	5.0b	(fma.f64 x (.f64 (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	29.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	32.1b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.8b	(fma.f64 x (sin.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cos.f64 y)))))

Compiler

Compiled 4007 to 1141 computations (71.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.3b	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.4b	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cos.f64 y)))
	0.6b	(cbrt.f64 z)

series286.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

266.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cos.f64 y)))
20.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cos.f64 y))))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 49

Calls

2 calls:

9.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cos.f64 y)))
8.0ms	(.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cos.f64 y))))

simplify141.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-neg_binary64`
582×	`cancel-sign-sub-inv_binary64`
545×	`fma-def_binary64`
528×	`unswap-sqr_binary64`
345×	`*-commutative_binary64`

Counts

97 → 92

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1558
1	245	1316
2	743	1078
3	1454	1061
4	3054	1037
5	4751	1037
6	4861	1037
7	4992	1037
8	4967	1037

prune164.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
	5.0b	(fma.f64 x (.f64 (pow.f64 (pow.f64 (sin.f64 y) 2) 1/3) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	29.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	32.1b	(fma.f64 x (exp.f64 (log.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	31.6b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 (cbrt.f64 z))) (.f64 (cbrt.f64 (cbrt.f64 z)) (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.8b	(fma.f64 x (sin.f64 y) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cos.f64 y)))))

Compiler

Compiled 3851 to 1125 computations (70.8% saved)

regimes1.2s (13.5%)

Accuracy

Total 0.1b remaining (47.8%)

Threshold costs 0.1b (47.8%)

Counts

170 → 1

Compiler

Compiled 13508 to 7866 computations (41.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	12
1	18	12
2	15	12

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample3.6s (41.4%)

Algorithm

1×

intervals

Results

1.6s	1988×	body	1024	valid
630.0ms	4528×	body	128	valid
579.0ms	982×	body	512	valid
147.0ms	499×	body	256	valid
5.0ms	3×	body	2048	valid

Compiler

Compiled 210 to 116 computations (44.8% saved)

Details

analyze614.0ms (7%)

sample143.0ms (1.6%)

simplify15.0ms (0.2%)

prune5.0ms (0.1%)

localize18.0ms (0.2%)

series54.0ms (0.6%)

rewrite14.0ms (0.2%)

simplify174.0ms (2%)

prune118.0ms (1.3%)

localize21.0ms (0.2%)

series759.0ms (8.7%)

rewrite38.0ms (0.4%)

simplify190.0ms (2.2%)

prune311.0ms (3.6%)

localize20.0ms (0.2%)

series507.0ms (5.8%)

rewrite25.0ms (0.3%)

simplify144.0ms (1.6%)

prune146.0ms (1.7%)

localize10.0ms (0.1%)

series286.0ms (3.3%)

rewrite21.0ms (0.2%)

simplify141.0ms (1.6%)

prune164.0ms (1.9%)

regimes1.2s (13.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.6s (41.4%)

Profiling