Details

analyze375.0ms (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 29 to 22 computations (24.1% saved)

sample55.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 46 to 36 computations (21.7% 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 3537118876014453/562949953421312 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
✓	0.1b	(/.f32 u1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
✓	0.3b	(*.f32 3537118876014453/562949953421312 u2)

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cube-cbrt_binary32`
26×	`add-sqr-sqrt_binary32`
24×	`pow1_binary32`
20×	`add-exp-log_binary32`
20×	`add-cbrt-cube_binary32`

Counts

4 → 164

Calls

4 calls:

18.0ms	(/.f32 u1 (-.f32 1 u1))
14.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
12.0ms	(*.f32 3537118876014453/562949953421312 u2)
10.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))

series54.0ms (0.7%)

Counts

4 → 40

Calls

4 calls:

38.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
8.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
6.0ms	(*.f32 3537118876014453/562949953421312 u2)
2.0ms	(/.f32 u1 (-.f32 1 u1))

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary32`
334×	`unswap-sqr_binary32`
241×	`prod-exp_binary32`
226×	`fma-neg_binary32`
186×	`cancel-sign-sub-inv_binary32`

Counts

204 → 292

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	2861
1	612	2696
2	2316	2641
3	4273	2635
4	4980	2635

prune278.0ms (3.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	278	14	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	279	14	293

Error

0.0b

Counts

293 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	6.6b	(-.f32 (exp.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) 1)
	1.5b	(.f32 (sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (/.f32 u1 (-.f32 1 u1))) (/.f32 u1 (-.f32 1 u1))) 1/3)) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.5b	(.f32 (cbrt.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (pow.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) 2))) (cbrt.f32 (.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.4b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.4b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
▶	0.3b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))
	3.0b	(-.f32 (+.f32 (.f32 52176791413089013764466731484482374711763629368301021948215227/803469022129495137770981046170581301261101496891396417650688 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 12511209943057747334229864889209/633825300114114700748351602688 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	6.6b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))) 3)
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))
	3.4b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) 3) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))

Compiler

Compiled 4486 to 3434 computations (23.5% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))
✓	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))
✓	0.3b	(.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))
✓	0.4b	(*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`pow1_binary32`
30×	`add-sqr-sqrt_binary32`
22×	`add-exp-log_binary32`
19×	`add-cube-cbrt_binary32`
18×	`add-cbrt-cube_binary32`

Counts

4 → 148

Calls

4 calls:

14.0ms	(sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))
13.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))
13.0ms	(.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))
11.0ms	(*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)

series59.0ms (0.7%)

Counts

4 → 56

Calls

4 calls:

38.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))
9.0ms	(.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))
6.0ms	(sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))
6.0ms	(*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

417×	`*-commutative_binary32`
393×	`prod-exp_binary32`
363×	`fma-neg_binary32`
288×	`unswap-sqr_binary32`
271×	`fma-def_binary32`

Counts

204 → 333

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	2541
1	440	2374
2	1461	2270
3	4215	2263
4	5370	2263

prune321.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	333	14	347

Error

0.0b

Counts

347 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	6.6b	(-.f32 (exp.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) 1)
	1.5b	(.f32 (sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (/.f32 u1 (-.f32 1 u1))) (/.f32 u1 (-.f32 1 u1))) 1/3)) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.5b	(.f32 (cbrt.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (pow.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) 2))) (cbrt.f32 (.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
▶	0.4b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	3.0b	(-.f32 (+.f32 (.f32 52176791413089013764466731484482374711763629368301021948215227/803469022129495137770981046170581301261101496891396417650688 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 12511209943057747334229864889209/633825300114114700748351602688 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	6.6b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))) 3)
	3.7b	(pow.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) 1/3)
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.4b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))
	3.4b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) 3) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))

Compiler

Compiled 4774 to 3536 computations (25.9% saved)

localize39.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
✓	0.2b	(log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2))))
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.3b	(*.f32 3537118876014453/562949953421312 u2)

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary32`
8×	`pow1_binary32`
8×	`add-sqr-sqrt_binary32`
6×	`add-cbrt-cube_binary32`
6×	`expm1-udef_binary32`

Counts

2 → 61

Calls

2 calls:

8.0ms

(expm1.f32 (log1p.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))))

8.0ms

(log1p.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2))))

series996.0ms (12.4%)

Counts

2 → 40

Calls

2 calls:

500.0ms

(expm1.f32 (log1p.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))))

496.0ms

(log1p.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2))))

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

555×	`distribute-rgt-in_binary32`
289×	`cancel-sign-sub-inv_binary32`
177×	`associate-/r*_binary32`
148×	`times-frac_binary32`
145×	`distribute-neg-in_binary32`

Counts

101 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	4477
1	671	4158
2	2864	3597
3	4989	3597

prune290.0ms (3.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	311	14	325

Error

0.0b

Counts

325 → 14

Alt Table

Status	Error	Program
	1.5b	(.f32 (sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (/.f32 u1 (-.f32 1 u1))) (/.f32 u1 (-.f32 1 u1))) 1/3)) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.5b	(.f32 (cbrt.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (pow.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) 2))) (cbrt.f32 (.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.4b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
▶	0.4b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
	0.8b	(expm1.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) 3))
	3.0b	(-.f32 (+.f32 (.f32 52176791413089013764466731484482374711763629368301021948215227/803469022129495137770981046170581301261101496891396417650688 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 12511209943057747334229864889209/633825300114114700748351602688 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	6.6b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	6.6b	(-.f32 (fma.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) 1) 1)
	0.4b	(.f32 (/.f32 (sqrt.f32 u1) (sqrt.f32 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	3.7b	(pow.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) 1/3)
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))
	3.4b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) 3) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))

Compiler

Compiled 6732 to 5428 computations (19.4% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 1 (-.f32 1 u1))
✓	0.2b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
✓	0.3b	(*.f32 u1 (/.f32 1 (-.f32 1 u1)))
	0.3b	(*.f32 3537118876014453/562949953421312 u2)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary32`
20×	`add-sqr-sqrt_binary32`
18×	`add-exp-log_binary32`
17×	`add-cbrt-cube_binary32`
14×	`pow1_binary32`

Counts

3 → 135

Calls

3 calls:

15.0ms	(/.f32 1 (-.f32 1 u1))
13.0ms	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
13.0ms	(*.f32 u1 (/.f32 1 (-.f32 1 u1)))

series39.0ms (0.5%)

Counts

3 → 44

Calls

3 calls:

35.0ms	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
2.0ms	(*.f32 u1 (/.f32 1 (-.f32 1 u1)))
2.0ms	(/.f32 1 (-.f32 1 u1))

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary32`
505×	`unswap-sqr_binary32`
335×	`prod-exp_binary32`
230×	`fma-neg_binary32`
158×	`associate-l_binary32`

Counts

179 → 280

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	2568
1	543	2370
2	2041	2248
3	4329	2247
4	5136	2247

prune297.0ms (3.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	373	1	374
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	374	14	388

Error

0.0b

Counts

388 → 14

Alt Table

Status	Error	Program
	0.4b	(/.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 u1)) (sqrt.f32 (-.f32 1 u1)))
	1.5b	(.f32 (sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (/.f32 u1 (-.f32 1 u1))) (/.f32 u1 (-.f32 1 u1))) 1/3)) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	0.5b	(.f32 (cbrt.f32 (.f32 (/.f32 u1 (-.f32 1 u1)) (pow.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) 2))) (cbrt.f32 (.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
✓	0.4b	(expm1.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
✓	0.4b	(.f32 (sqrt.f32 (.f32 u1 (/.f32 1 (-.f32 1 u1)))) (cos.f32 (*.f32 3537118876014453/562949953421312 u2)))
	0.8b	(expm1.f32 (pow.f32 (cbrt.f32 (log1p.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) 3))
	3.0b	(-.f32 (+.f32 (.f32 52176791413089013764466731484482374711763629368301021948215227/803469022129495137770981046170581301261101496891396417650688 (.f32 (pow.f32 u2 4) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 12511209943057747334229864889209/633825300114114700748351602688 (.f32 (pow.f32 u2 2) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	6.6b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))
	6.6b	(-.f32 (fma.f32 (cos.f32 (*.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) 1) 1)
	3.7b	(pow.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (sqrt.f32 (.f32 u2 (*.f32 u2 12511209943057747334229864889209/316912650057057350374175801344)))))) 1/3)
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))))
	0.4b	(.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (.f32 (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))) (cbrt.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2))))
	3.4b	(exp.f32 (log.f32 (.f32 (cos.f32 (.f32 3537118876014453/562949953421312 u2)) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) 3) (cos.f32 (.f32 3537118876014453/562949953421312 u2)))

Compiler

Compiled 4834 to 3788 computations (21.6% saved)

regimes2.4s (30.3%)

Accuracy

Total 0.2b remaining (75.1%)

Threshold costs 0.2b (75.1%)

Compiler

Compiled 40604 to 32275 computations (20.5% saved)

simplify4.0ms (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	26
1	22	26
2	26	26
3	28	26
4	29	26
5	28	26

end1.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

sample2.0s (25%)

Algorithm

1×

intervals

Results

923.0ms	8000×	body	128	valid
253.0ms	8000×	pre	128	true
0.0ms	1×	pre	128	false

Compiler

Compiled 390 to 308 computations (21% 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

analyze375.0ms (4.7%)

sample55.0ms (0.7%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize33.0ms (0.4%)

rewrite61.0ms (0.8%)

series54.0ms (0.7%)

simplify120.0ms (1.5%)

prune278.0ms (3.5%)

localize40.0ms (0.5%)

rewrite57.0ms (0.7%)

series59.0ms (0.7%)

simplify118.0ms (1.5%)

prune321.0ms (4%)

localize39.0ms (0.5%)

rewrite20.0ms (0.2%)

series996.0ms (12.4%)

simplify116.0ms (1.4%)

prune290.0ms (3.6%)

localize35.0ms (0.4%)

rewrite47.0ms (0.6%)

series39.0ms (0.5%)

simplify118.0ms (1.5%)

prune297.0ms (3.7%)

regimes2.4s (30.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.0s (25%)

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