Details

analyze248.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.6%	98.4%	0
0%	1.6%	98.4%	1
0%	1.6%	98.4%	2
0.4%	1.2%	98.4%	3
0.6%	1%	98.4%	4
0.9%	0.7%	98.4%	5
1%	0.5%	98.4%	6
1.2%	0.4%	98.4%	7
1.3%	0.3%	98.4%	8
1.4%	0.2%	98.4%	9
1.4%	0.1%	98.4%	10
1.5%	0.1%	98.4%	11
1.5%	0.1%	98.4%	12
1.5%	0%	98.4%	13
1.5%	0%	98.4%	14

Compiler

Compiled 54 to 41 computations (24.1% saved)

sample2.2s (12%)

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

Status

Error

Program

▶

0.3b

(*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (*.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 225 to 172 computations (23.6% saved)

localize69.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (/.f32 1 (+.f32 (*.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)
✓	0.2b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
✓	0.3b	(/.f32 (PI.f32) s)
✓	0.3b	(/.f32 (neg.f32 (PI.f32)) s)

series1.1s (5.7%)

Counts

4 → 60

Calls

4 calls:

872.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
175.0ms	(-.f32 (/.f32 1 (+.f32 (*.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)
5.0ms	(/.f32 (PI.f32) s)
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)

rewrite48.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary32`
238×	`log1p-expm1-u_binary32`
238×	`expm1-log1p-u_binary32`
235×	`add-log-exp_binary32`
232×	`add-exp-log_binary32`

Counts

4 → 82

Calls

4 calls:

45.0ms	(-.f32 (/.f32 1 (+.f32 (*.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)
45.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
45.0ms	(/.f32 (PI.f32) s)
45.0ms	(/.f32 (neg.f32 (PI.f32)) s)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	123
1	497	123
2	4947	123
0	0	0
1	0	0

prune346.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	154	10	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	10	165

Error

0.1b

Counts

165 → 10

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 3)
	0.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1) 3) 1/3)))
	1.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) (sqrt.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	31.3b	(pow.f32 (sqrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 2)
	0.3b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))))
▶	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
	0.3b	(.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (fma.f32 (sqrt.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) (sqrt.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))
	16.7b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)) 3)))

Compiler

Compiled 11392 to 7058 computations (38% saved)

localize95.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
✓	0.3b	(/.f32 (PI.f32) s)
✓	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	3.1b	(exp.f32 (log.f32 (/.f32 (PI.f32) s)))

series929.0ms (5%)

Counts

4 → 48

Calls

4 calls:

921.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
3.0ms	(exp.f32 (log.f32 (/.f32 (PI.f32) s)))
2.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(/.f32 (PI.f32) s)

rewrite42.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

262×	`add-sqr-sqrt_binary32`
249×	`log1p-expm1-u_binary32`
249×	`expm1-log1p-u_binary32`
245×	`add-log-exp_binary32`
242×	`add-exp-log_binary32`

Counts

4 → 88

Calls

4 calls:

39.0ms	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
39.0ms	(/.f32 (PI.f32) s)
39.0ms	(/.f32 (neg.f32 (PI.f32)) s)
39.0ms	(exp.f32 (log.f32 (/.f32 (PI.f32) s)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	76
1	523	76
2	5095	76
0	0	0
1	0	0

prune409.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	161	10	171

Error

0.1b

Counts

171 → 10

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 3)
	0.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1) 3) 1/3)))
	1.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) (sqrt.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	31.3b	(pow.f32 (sqrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 2)
▶	0.3b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
	0.3b	(.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (expm1.f32 (neg.f32 (log.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (fma.f32 (sqrt.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) (sqrt.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))
	16.7b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)) 3)))

Compiler

Compiled 9907 to 6062 computations (38.8% saved)

localize83.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))))
✓	0.3b	(/.f32 (PI.f32) s)
✓	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	1.8b	(pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

series2.6s (14.2%)

Counts

4 → 60

Calls

4 calls:

1.9s	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))))
676.0ms	(pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
3.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(/.f32 (PI.f32) s)

rewrite78.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary32`
235×	`log1p-expm1-u_binary32`
235×	`expm1-log1p-u_binary32`
234×	`add-log-exp_binary32`
229×	`add-exp-log_binary32`

Counts

4 → 79

Calls

4 calls:

74.0ms	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))))
74.0ms	(/.f32 (PI.f32) s)
74.0ms	(/.f32 (neg.f32 (PI.f32)) s)
74.0ms	(pow.f32 (E.f32) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	123
1	495	123
2	4891	123
3	5093	123
0	0	0
1	0	0

prune358.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	164	7	171

Error

0.1b

Counts

171 → 7

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 3)
	0.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1) 3) 1/3)))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (fma.f32 (cbrt.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2)) (/.f32 1 (cbrt.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))
	1.0b	(.f32 (neg.f32 s) (log.f32 (.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))) (pow.f32 (cbrt.f32 (E.f32)) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
▶	0.3b	(.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	16.7b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)) 3)))

Compiler

Compiled 11234 to 6899 computations (38.6% saved)

localize101.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
✓	0.3b	(/.f32 (PI.f32) s)
✓	0.3b	(/.f32 (neg.f32 (PI.f32)) s)
✓	0.4b	(/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))

series7.4s (39.6%)

Counts

4 → 60

Calls

4 calls:

7.0s	(/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))
346.0ms	(+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
2.0ms	(/.f32 (neg.f32 (PI.f32)) s)
2.0ms	(/.f32 (PI.f32) s)

rewrite68.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

286×	`log1p-expm1-u_binary32`
286×	`expm1-log1p-u_binary32`
276×	`add-log-exp_binary32`
273×	`add-exp-log_binary32`
272×	`add-cbrt-cube_binary32`

Counts

4 → 84

Calls

4 calls:

63.0ms	(+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))
63.0ms	(/.f32 (PI.f32) s)
63.0ms	(/.f32 (neg.f32 (PI.f32)) s)
63.0ms	(/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (*.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	272
1	593	272
2	5030	272
0	0	0
1	0	0

prune1.4s (7.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	310	7	317

Error

0.1b

Counts

317 → 7

Alt Table

Status	Error	Program
	0.7b	(pow.f32 (cbrt.f32 (*.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)))) 3)
	0.4b	(*.f32 (neg.f32 s) (log.f32 (pow.f32 (pow.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1) 3) 1/3)))
	0.3b	(*.f32 (neg.f32 s) (log.f32 (fma.f32 (cbrt.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2)) (/.f32 1 (cbrt.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) -1)))
	1.0b	(.f32 (neg.f32 s) (log.f32 (.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))) (pow.f32 (cbrt.f32 (E.f32)) (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (-.f32 (/.f32 1 (+.f32 (.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (/.f32 1 (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) 1)))
✓	0.3b	(.f32 (neg.f32 s) (log.f32 (/.f32 (-.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -3) 1) (+.f32 (pow.f32 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) -2) (+.f32 1 (.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))))
	16.7b	(cbrt.f32 (*.f32 (pow.f32 (neg.f32 s) 3) (pow.f32 (log.f32 (-.f32 (/.f32 1 (fma.f32 u (-.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1)) 3)))

Compiler

Compiled 53978 to 31488 computations (41.7% saved)

regimes762.0ms (4.1%)

Accuracy

Total 0.2b remaining (66.6%)

Threshold costs 0.2b (66.6%)

Counts

144 → 1

Compiler

Compiled 20343 to 15599 computations (23.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary32`
9×	`*-commutative_binary32`
8×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	65
1	47	65
2	63	65
3	74	65
4	79	65
5	80	65
6	78	65

end290.0ms (1.6%)

Compiler: Compiled 503 to 369 computations (26.6% saved)

Details

analyze248.0ms (1.3%)

sample2.2s (12%)

localize69.0ms (0.4%)

series1.1s (5.7%)

rewrite48.0ms (0.3%)

prune346.0ms (1.9%)

localize95.0ms (0.5%)

series929.0ms (5%)

rewrite42.0ms (0.2%)

prune409.0ms (2.2%)

localize83.0ms (0.4%)

series2.6s (14.2%)

rewrite78.0ms (0.4%)

prune358.0ms (1.9%)

localize101.0ms (0.5%)

series7.4s (39.6%)

rewrite68.0ms (0.4%)

prune1.4s (7.4%)

regimes762.0ms (4.1%)

simplify4.0ms (0%)

end290.0ms (1.6%)

Profiling