Details

analyze409.0ms (4.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 37 to 28 computations (24.3% saved)

sample2.0s (22.6%)

Results

1.9s	8256×	body	128	valid
3.0ms	7×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary32`
7×	`+-commutative_binary32`
6×	`fma-def_binary32`
4×	`*-commutative_binary32`
4×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (*.f32 314159265359/50000000000 u2))
✓	0.1b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.3b	(*.f32 314159265359/50000000000 u2)

series31.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

25.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
3.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(cos.f32 (*.f32 314159265359/50000000000 u2))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary32`
50×	`*-un-lft-identity_binary32`
37×	`times-frac_binary32`
30×	`associate-l_binary32`
29×	`add-cube-cbrt_binary32`

Counts

4 → 119

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
4.0ms	(/.f32 u1 (-.f32 1 u1))
4.0ms	(*.f32 314159265359/50000000000 u2)
1.0ms	(cos.f32 (*.f32 314159265359/50000000000 u2))

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-l_binary32`
431×	`fma-def_binary32`
378×	`associate-/r*_binary32`
357×	`times-frac_binary32`
249×	`associate-/l*_binary32`

Counts

155 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	2854
1	565	2690
2	1637	2568
3	4598	2568
4	4961	2568

prune264.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	183	9	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	9	193

Error

0.0b

Counts

193 → 9

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	0.3b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2))))) (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (log.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 1 (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1)))) (/.f32 u1 (cbrt.f32 (-.f32 1 u1))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (cos.f32 (.f32 314159265359/50000000000 u2)))))

Compiler

Compiled 4254 to 3130 computations (26.4% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))
✓	0.1b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.3b	(.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2))

series55.0ms (0.6%)

Counts

3 → 44

Calls

3 calls:

40.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))

10.0ms

(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

5.0ms

(cos.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`associate-l_binary32`
33×	`add-sqr-sqrt_binary32`
29×	`sqrt-prod_binary32`
26×	`*-un-lft-identity_binary32`
19×	`times-frac_binary32`

Counts

3 → 79

Calls

3 calls:

11.0ms

(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))

5.0ms

(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

2.0ms

(cos.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

523×	`fma-neg_binary32`
389×	`fma-def_binary32`
330×	`*-commutative_binary32`
299×	`associate-/r*_binary32`
257×	`unswap-sqr_binary32`

Counts

123 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	2277
1	487	2121
2	1411	1968
3	3769	1960
4	4991	1960
5	4934	1960

prune274.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	5	215
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	216	8	224

Error

0.0b

Counts

224 → 8

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (expm1.f32 (log1p.f32 (cos.f32 (.f32 u2 314159265359/50000000000)))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	2.2b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (cos.f32 (.f32 u2 314159265359/50000000000)))) (sqrt.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (log.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))))

Compiler

Compiled 5201 to 4030 computations (22.5% saved)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(expm1.f32 (log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000))))
✓	0.2b	(log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)))
✓	0.3b	(*.f32 u2 314159265359/50000000000)

series202.0ms (2.3%)

Counts

3 → 36

Calls

3 calls:

198.0ms	(log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)))
2.0ms	(expm1.f32 (log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000))))
2.0ms	(*.f32 u2 314159265359/50000000000)

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-cube-cbrt_binary32`
5×	`add-cbrt-cube_binary32`
5×	`add-exp-log_binary32`

Counts

3 → 42

Calls

3 calls:

51.0ms	(*.f32 u2 314159265359/50000000000)
0.0ms	(log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)))
0.0ms	(expm1.f32 (log1p.f32 (cos.f32 (*.f32 u2 314159265359/50000000000))))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-def_binary32`
485×	`sub-neg_binary32`
344×	`distribute-rgt-neg-in_binary32`
326×	`cancel-sign-sub-inv_binary32`
260×	`fma-neg_binary32`

Counts

78 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	647
1	167	601
2	390	595
3	1017	591
4	2253	591
5	3492	591
6	4581	591
7	4954	591
8	4815	591

prune184.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Error

0.0b

Counts

152 → 8

Alt Table

Status	Error	Program
	2.2b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (cos.f32 (.f32 u2 314159265359/50000000000)))) (sqrt.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	3.1b	(exp.f32 (+.f32 (log.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (log.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))))
▶	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (expm1.f32 (log.f32 (+.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 1))))

Compiler

Compiled 2989 to 2279 computations (23.8% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(expm1.f32 (log.f32 (+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)))
✓	0.3b	(+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)
	0.3b	(*.f32 314159265359/50000000000 u2)

series201.0ms (2.3%)

Counts

2 → 20

Calls

2 calls:

199.0ms	(expm1.f32 (log.f32 (+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)))
2.0ms	(+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary32`
4×	`add-log-exp_binary32`
3×	`add-sqr-sqrt_binary32`
3×	`fma-def_binary32`
3×	`add-cube-cbrt_binary32`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)
0.0ms	(expm1.f32 (log.f32 (+.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 1)))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary32`
322×	`distribute-rgt-neg-in_binary32`
298×	`unswap-sqr_binary32`
276×	`distribute-lft-neg-in_binary32`
258×	`associate-l_binary32`

Counts

48 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	592
1	146	505
2	296	458
3	739	452
4	2280	452
5	4640	452
6	4937	452
7	4934	452

prune176.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	145	8	153

Error

0.0b

Counts

153 → 8

Alt Table

Status	Error	Program
	2.2b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (cos.f32 (.f32 u2 314159265359/50000000000)))) (sqrt.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (.f32 (sqrt.f32 314159265359/50000000000) u2)))))
	0.8b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (log.f32 (exp.f32 (cos.f32 (.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))))
	0.6b	(.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
	6.1b	(log.f32 (exp.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))))
	0.5b	(.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1)))) (.f32 (cos.f32 (*.f32 u2 314159265359/50000000000)) (sqrt.f32 (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))))
✓	0.4b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (expm1.f32 (log.f32 (+.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 1))))
	1.2b	(.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (expm1.f32 (log.f32 (+.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 1))))

Compiler

Compiled 3139 to 2464 computations (21.5% saved)

regimes4.0s (46.8%)

Accuracy

Total 0.2b remaining (77%)

Threshold costs 0.2b (77%)

Counts

373 → 1

Compiler

Compiled 71811 to 56836 computations (20.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	22	28
2	26	28
3	28	28
4	29	28
5	28	28

end140.0ms (1.6%)

Compiler: Compiled 224 to 181 computations (19.2% saved)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Details

analyze409.0ms (4.7%)

sample2.0s (22.6%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize29.0ms (0.3%)

series31.0ms (0.4%)

rewrite27.0ms (0.3%)

simplify104.0ms (1.2%)

prune264.0ms (3.1%)

localize37.0ms (0.4%)

series55.0ms (0.6%)

rewrite24.0ms (0.3%)

simplify115.0ms (1.3%)

prune274.0ms (3.2%)

localize43.0ms (0.5%)

series202.0ms (2.3%)

rewrite52.0ms (0.6%)

simplify115.0ms (1.3%)

prune184.0ms (2.1%)

localize48.0ms (0.6%)

series201.0ms (2.3%)

rewrite4.0ms (0%)

simplify89.0ms (1%)

prune176.0ms (2%)

regimes4.0s (46.8%)

simplify3.0ms (0%)

end140.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17