Details

analyze1.1s (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	90.4%	9.6%	9
0%	45.2%	54.8%	10
0%	45.2%	54.8%	11
0%	45.2%	54.8%	12
0%	45.2%	54.8%	13
0%	44.4%	55.6%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.3s (36.4%)

Results

3.2s	16864×	body	128	invalid
1.5s	7569×	body	128	valid
169.0ms	309×	body	512	valid
119.0ms	131×	body	1024	valid
92.0ms	247×	body	256	valid
72.0ms	127×	body	512	invalid
45.0ms	44×	body	1024	invalid
43.0ms	119×	body	256	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
557×	`associate-/l*_binary64`
456×	`unswap-sqr_binary64`
365×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	34	25
2	73	25
3	158	25
4	405	25
5	1252	25
6	2771	25
7	4527	25
8	5117	25

prune4.0ms (0%)

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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 84 to 54 computations (35.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
✓	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
✓	0.6b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.2s (8%)

Counts

4 → 164

Calls

4 calls:

507.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
326.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
291.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
45.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 95

Calls

4 calls:

5.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
4.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
1.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
0.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify224.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
292×	`*-commutative_binary64`
185×	`sub-neg_binary64`
182×	`times-frac_binary64`
175×	`associate-r_binary64`

Counts

259 → 297

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	713	11258
1	2189	10188
2	4843	10188
3	4989	10188

prune345.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	292	5	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	5	298

Error

0.1b

Counts

298 → 5

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 x (.f64 (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (cbrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	4.9b	(expm1.f64 (log1p.f64 (.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))))
▶	0.6b	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	12.7b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))
	17.1b	(.f64 x (exp.f64 (.f64 (-.f64 (log.f64 z) t) y)))

Compiler

Compiled 13917 to 5267 computations (62.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
	0.6b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series867.0ms (5.9%)

Counts

2 → 132

Calls

2 calls:

818.0ms	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
48.0ms	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`unpow-prod-down_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(.f64 x (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
2.0ms	(pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify259.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-l_binary64`
567×	`fma-def_binary64`
250×	`*-commutative_binary64`
170×	`times-frac_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

182 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	524	10089
1	1716	9313
2	4966	9313
3	5018	9313

prune515.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	324	3	327
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	328	4	332

Error

0.0b

Counts

332 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 x (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	0.6b	(.f64 (.f64 x (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
▶	0.1b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
	12.7b	(.f64 x (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a b (.f64 y t)))))

Compiler

Compiled 15018 to 5354 computations (64.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (+.f64 b z) (*.f64 y t))
✓	0.0b	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))
✓	0.1b	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
✓	0.2b	(*.f64 (log.f64 z) y)

series501.0ms (3.4%)

Counts

4 → 188

Calls

4 calls:

251.0ms	(*.f64 (log.f64 z) y)
197.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))
36.0ms	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
17.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
7×	`unpow-prod-up_binary64`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
3.0ms	(-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))
3.0ms	(*.f64 (log.f64 z) y)
0.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

simplify139.0ms (1%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-r_binary64`
388×	`fma-neg_binary64`
348×	`associate-l_binary64`
279×	`fma-def_binary64`
211×	`*-commutative_binary64`

Counts

268 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	5800
1	913	5526
2	3542	5431
3	4928	5431

prune265.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	209	4	213

Error

0.0b

Counts

213 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 x (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
▶	0.6b	(.f64 (.f64 x (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	11.8b	(.f64 x (expm1.f64 (log1p.f64 (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a (+.f64 z b) (.f64 y t)))))))
✓	0.1b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))

Compiler

Compiled 6677 to 1540 computations (76.9% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.1b	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
	0.6b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series1.2s (8.4%)

Counts

2 → 132

Calls

2 calls:

1.1s

(*.f64 (*.f64 x (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

89.0ms

(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
12×	`unpow-prod-down_binary64`
11×	`associate-r_binary64`
8×	`pow-exp_binary64`

Counts

2 → 62

Calls

2 calls:

8.0ms

(*.f64 (*.f64 x (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

2.0ms

(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify297.0ms (2%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-def_binary64`
439×	`*-commutative_binary64`
331×	`associate-r_binary64`
322×	`times-frac_binary64`
205×	`associate-/l*_binary64`

Counts

194 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	770	14327
1	2522	13670
2	4992	13670
3	4997	13670

prune849.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	552	1	553
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	553	4	557

Error

0.0b

Counts

557 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 x (sqrt.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (sqrt.f64 (pow.f64 (E.f64) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	11.8b	(.f64 x (expm1.f64 (log1p.f64 (/.f64 (pow.f64 z y) (exp.f64 (fma.f64 a (+.f64 z b) (.f64 y t)))))))
✓	0.1b	(.f64 x (pow.f64 (E.f64) (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))))
	0.6b	(.f64 (.f64 x (.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))) (cbrt.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))) (pow.f64 (sqrt.f64 (E.f64)) (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

Compiler

Compiled 37711 to 11946 computations (68.3% saved)

regimes1.2s (8.5%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Counts

143 → 1

Compiler

Compiled 32492 to 20688 computations (36.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	21	24
2	26	24
3	28	24
4	29	24
5	29	24

end82.0ms (0.6%)

Compiler: Compiled 208 to 99 computations (52.4% saved)

Details

analyze1.1s (7.6%)

sample5.3s (36.4%)

simplify51.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series1.2s (8%)

rewrite18.0ms (0.1%)

simplify224.0ms (1.5%)

prune345.0ms (2.4%)

localize16.0ms (0.1%)

series867.0ms (5.9%)

rewrite9.0ms (0.1%)

simplify259.0ms (1.8%)

prune515.0ms (3.5%)

localize17.0ms (0.1%)

series501.0ms (3.4%)

rewrite18.0ms (0.1%)

simplify139.0ms (1%)

prune265.0ms (1.8%)

localize37.0ms (0.3%)

series1.2s (8.4%)

rewrite17.0ms (0.1%)

simplify297.0ms (2%)

prune849.0ms (5.8%)

regimes1.2s (8.5%)

simplify3.0ms (0%)

end82.0ms (0.6%)

Profiling