Details

analyze766.0ms (2.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	99.9%	4
0%	0%	99.9%	5
0%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 41 to 30 computations (26.8% saved)

sample65.0ms (0.2%)

Algorithm

1×

intervals

Results

33.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 72 to 53 computations (26.4% saved)

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-+l-_binary32`
416×	`associate-+r-_binary32`
386×	`associate--l-_binary32`
320×	`neg-mul-1_binary32`
316×	`distribute-rgt-in_binary32`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	39
2	113	39
3	402	39
4	1502	36
5	4687	36
6	4944	36
7	5024	36

prune62.0ms (0.2%)

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

0.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	13.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))

Status

Error

Program

▶

0.6b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (*.f32 (-.f32 ux (*.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1))))

13.1b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) PI.f32)) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

Compiler

Compiled 134 to 94 computations (29.9% saved)

localize59.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
0.2b	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))

rewrite250.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-log-exp_binary32`
11×	`add-cbrt-cube_binary32`
11×	`add-exp-log_binary32`
11×	`pow1_binary32`
10×	`associate-*r/_binary32`

Counts

4 → 68

Calls

4 calls:

14.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
7.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
5.0ms	(.f32 (.f32 uy 2) PI.f32)
1.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))

Compiler

Compiled 2292 to 1268 computations (44.7% saved)

series222.0ms (0.6%)

Error

0.4b

Counts

4 → 36

Calls

4 calls:

110.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
28.0ms	(+.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) 1)
15.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
10.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3199 to 2169 computations (32.2% saved)

simplify146.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

408×	`cancel-sign-sub-inv_binary32`
382×	`associate-l_binary32`
341×	`associate-r_binary32`
302×	`times-frac_binary32`
217×	`*-commutative_binary32`

Counts

104 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	3451
1	772	3058
2	2902	2836
3	4543	2797
4	5035	2797

prune241.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	66	10	76

Error

0.1b

Counts

76 → 10

Alt Table

Status	Error	Program
	19.4b	(log.f32 (exp.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (+.f32 1 (pow.f32 (+.f32 (.f32 maxCos ux) (-.f32 1 ux)) 3)) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (+.f32 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))) (-.f32 (.f32 1 1) (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	0.9b	(.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1)))))
▶	0.6b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	1.6b	(.f32 (sin.f32 (exp.f32 (log.f32 (.f32 2 (.f32 uy PI.f32))))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	1.0b	(.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (cbrt.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))))))
	1.7b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux)))))))) (cbrt.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 3207 to 1768 computations (44.9% saved)

localize70.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
0.3b	(.f32 (.f32 uy 2) PI.f32)
0.4b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
0.7b	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))

rewrite331.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

74×	`sqrt-div_binary32`
42×	`associate-*r/_binary32`
41×	`add-sqr-sqrt_binary32`
33×	`flip--_binary32`
33×	`flip3--_binary32`

Counts

4 → 137

Calls

4 calls:

25.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
15.0ms	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))
4.0ms	(.f32 (.f32 uy 2) PI.f32)
2.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))

Compiler

Compiled 5901 to 2697 computations (54.3% saved)

series218.0ms (0.6%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

107.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
30.0ms	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))
19.0ms	(sin.f32 (.f32 (.f32 uy 2) PI.f32))
12.0ms	(.f32 (.f32 uy 2) PI.f32)

Compiler

Compiled 3351 to 2235 computations (33.3% saved)

simplify172.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-l_binary32`
445×	`associate-r_binary32`
406×	`cancel-sign-sub-inv_binary32`
293×	`*-commutative_binary32`
288×	`neg-mul-1_binary32`

Counts

173 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	382	5563
1	859	5126
2	3136	4924
3	4465	4869
4	5069	4869

prune272.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	8	140
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	140	10	150

Error

0.0b

Counts

150 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) 1))))
	1.7b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (pow.f32 (sqrt.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux))) 3)))))
▶	0.6b	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (+.f32 ux (.f32 maxCos ux)) (-.f32 (.f32 4 (-.f32 ux (.f32 maxCos ux))) (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (+.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 5145 to 2545 computations (50.5% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(sin.f32 (.f32 (.f32 2 uy) PI.f32))
0.3b	(.f32 (.f32 2 uy) PI.f32)
0.4b	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
0.7b	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))

rewrite323.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

74×	`sqrt-div_binary32`
42×	`associate-*r/_binary32`
41×	`add-sqr-sqrt_binary32`
33×	`flip--_binary32`
33×	`flip3--_binary32`

Counts

4 → 137

Calls

4 calls:

23.0ms	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
14.0ms	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))
4.0ms	(.f32 (.f32 2 uy) PI.f32)
2.0ms	(sin.f32 (.f32 (.f32 2 uy) PI.f32))

Compiler

Compiled 5901 to 2697 computations (54.3% saved)

series259.0ms (0.7%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

152.0ms	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
28.0ms	(.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 maxCos ux)))))
19.0ms	(sin.f32 (.f32 (.f32 2 uy) PI.f32))
12.0ms	(.f32 (.f32 2 uy) PI.f32)

Compiler

Compiled 3351 to 2235 computations (33.3% saved)

simplify191.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

444×	`associate-l_binary32`
442×	`associate-r_binary32`
406×	`cancel-sign-sub-inv_binary32`
293×	`*-commutative_binary32`
288×	`neg-mul-1_binary32`

Counts

173 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	381	5563
1	859	5126
2	3111	4924
3	4463	4869
4	5060	4869

prune206.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Error

0.0b

Counts

148 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (+.f32 ux (.f32 maxCos ux)) (-.f32 (.f32 4 (-.f32 ux (.f32 maxCos ux))) (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (+.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (/.f32 (-.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux)))) (+.f32 2 (-.f32 ux (*.f32 maxCos ux)))))))
	1.7b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (pow.f32 (sqrt.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux))) 3)))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux)))))) (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))))
▶	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 5014 to 2468 computations (50.8% saved)

localize120.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)))))))
0.3b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
0.3b	(*.f32 uy PI.f32)
0.6b	(.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (*.f32 maxCos ux)) 3))))

rewrite662.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

140×	`sqrt-div_binary32`
82×	`associate-*r/_binary32`
60×	`flip--_binary32`
60×	`frac-times_binary32`
60×	`flip3--_binary32`

Counts

4 → 171

Calls

4 calls:

36.0ms	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
25.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)))))))
17.0ms	(.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (*.f32 maxCos ux)) 3))))
3.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 13789 to 6315 computations (54.2% saved)

series16.2s (43.4%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

14.4s	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
670.0ms	(.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)))))))
169.0ms	(.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (*.f32 maxCos ux)) 3))))
17.0ms	(*.f32 uy PI.f32)

Compiler

Compiled 50264 to 39263 computations (21.9% saved)

simplify1.0s (2.7%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-r_binary32`
411×	`associate-+r+_binary32`
298×	`associate-l_binary32`
80×	`sqr-pow_binary32`
55×	`sub-neg_binary32`

Counts

218 → 136

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2149	42486
1	5120	42486

prune1.2s (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	136	9	145

Error

0.0b

Counts

145 → 9

Alt Table

Status	Error	Program
	0.8b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (+.f32 ux (.f32 maxCos ux)) (-.f32 (.f32 4 (-.f32 ux (.f32 maxCos ux))) (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))) (sqrt.f32 (.f32 (+.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (+.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (+.f32 2 (-.f32 ux (*.f32 maxCos ux))))))))
	0.6b	(.f32 (sin.f32 (.f32 (.f32 2 uy) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (/.f32 (-.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux)))) (+.f32 2 (-.f32 ux (*.f32 maxCos ux)))))))
	1.7b	(.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32))) (.f32 (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (sin.f32 (.f32 2 (*.f32 uy PI.f32))))))
	0.8b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))) (pow.f32 (sqrt.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux))) 3)))))
	0.7b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux) (.f32 ux (-.f32 ux (.f32 maxCos (.f32 maxCos ux))))))) (sqrt.f32 (+.f32 ux (*.f32 ux maxCos))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))) (-.f32 (pow.f32 ux 3) (pow.f32 (.f32 maxCos ux) 3))))) (sqrt.f32 (+.f32 (.f32 ux ux) (+.f32 (.f32 (.f32 ux maxCos) (.f32 ux maxCos)) (.f32 ux (.f32 ux maxCos))))))
	0.7b	(.f32 (/.f32 (sin.f32 (.f32 2 (.f32 uy PI.f32))) (fabs.f32 (cbrt.f32 (sqrt.f32 (+.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (+.f32 (-.f32 ux (.f32 maxCos ux)) 2))))))) (/.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3)))))) (sqrt.f32 (cbrt.f32 (sqrt.f32 (+.f32 4 (.f32 (-.f32 ux (.f32 maxCos ux)) (+.f32 (-.f32 ux (.f32 maxCos ux)) 2))))))))
	0.6b	(/.f32 (.f32 (sin.f32 (.f32 2 (cbrt.f32 (.f32 (pow.f32 uy 3) (pow.f32 PI.f32 3))))) (sqrt.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (.f32 (sqrt.f32 (-.f32 (+.f32 2 (.f32 maxCos ux)) ux)) (sqrt.f32 (-.f32 8 (pow.f32 (-.f32 ux (.f32 maxCos ux)) 3))))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 2 2) (+.f32 (.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 ux (.f32 maxCos ux))) (.f32 2 (-.f32 ux (.f32 maxCos ux))))))))
	0.9b	(.f32 (sin.f32 (.f32 (.f32 (.f32 2 uy) (.f32 (cbrt.f32 PI.f32) (cbrt.f32 PI.f32))) (cbrt.f32 PI.f32))) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux)))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 maxCos ux))))))))

Compiler

Compiled 28713 to 18859 computations (34.3% saved)

regimes11.6s (31.1%)

Accuracy

Total 0.4b remaining (87%)

Threshold costs 0.4b (87%)

Compiler

Compiled 199936 to 124796 computations (37.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	37	44
2	46	44
3	52	44
4	56	44
5	57	44
6	56	44

end1.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

sample2.5s (6.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
269.0ms	8000×	pre	128	true

Compiler

Compiled 503 to 310 computations (38.4% saved)

Details

analyze766.0ms (2.1%)

sample65.0ms (0.2%)

simplify66.0ms (0.2%)

prune62.0ms (0.2%)

localize59.0ms (0.2%)

rewrite250.0ms (0.7%)

series222.0ms (0.6%)

simplify146.0ms (0.4%)

prune241.0ms (0.6%)

localize70.0ms (0.2%)

rewrite331.0ms (0.9%)

series218.0ms (0.6%)

simplify172.0ms (0.5%)

prune272.0ms (0.7%)

localize74.0ms (0.2%)

rewrite323.0ms (0.9%)

series259.0ms (0.7%)

simplify191.0ms (0.5%)

prune206.0ms (0.6%)

localize120.0ms (0.3%)

rewrite662.0ms (1.8%)

series16.2s (43.4%)

simplify1.0s (2.7%)

prune1.2s (3.2%)

regimes11.6s (31.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.5s (6.6%)

Profiling