Details

analyze1.8s (5.3%)

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%	99.7%	0.3%	9
0%	49.9%	50.1%	10
0%	49.9%	50.1%	11
0%	49.9%	50.1%	12
0%	49.9%	50.1%	13
0%	49.9%	50.1%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample5.1s (15.3%)

Results

2.4s	8383×	body	128	invalid
2.2s	7673×	body	128	valid
200.0ms	248×	body	512	valid
138.0ms	104×	body	1024	valid
111.0ms	231×	body	256	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify62.0ms (0.2%)

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(.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%)

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	(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))
✓	1.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series2.0s (5.9%)

Counts

4 → 164

Calls

4 calls:

884.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
510.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
461.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
108.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite40.0ms (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:

16.0ms	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
8.0ms	(.f64 x (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
2.0ms	(exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))
1.0ms	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

simplify438.0ms (1.3%)

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

prune420.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	3	298

Error

0.0b

Counts

298 → 3

Alt Table

Status	Error	Program
	1.0b	(.f64 x (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) 3)))
	1.4b	(.f64 x (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (*.f64 y t)))))
▶	1.0b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))

Compiler

Compiled 13841 to 5217 computations (62.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))
	1.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))
✓	18.1b	(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

series11.8s (35.4%)

Counts

2 → 120

Calls

2 calls:

11.3s

(*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

556.0ms

(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

10.0ms

(*.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))

1.0ms

(cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))

simplify1.0s (3.1%)

Algorithm

1×	egg-herbie

Counts

175 → 171

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5217	81535

prune3.8s (11.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	730	1	731
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	731	3	734

Error

0.0b

Counts

734 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
	1.1b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a b (.f64 y t))))))
▶	1.0b	(.f64 x (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) 3)))

Compiler

Compiled 103967 to 52302 computations (49.7% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) 3))
	0.0b	(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))
	1.1b	(fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))

series102.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

102.0ms

(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) 3))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
4×	`cube-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) 3))

simplify238.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

626×	`times-frac_binary64`
387×	`associate-r_binary64`
359×	`fma-neg_binary64`
291×	`fma-def_binary64`
273×	`associate-l_binary64`

Counts

85 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	4822
1	955	4387
2	3765	4282
3	5165	4282

prune820.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	299	2	301

Error

0.0b

Counts

301 → 2

Alt Table

Status	Error	Program
✓	1.0b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
▶	0.5b	(.f64 x (cbrt.f64 (pow.f64 (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))) 3)))

Status

Error

Program

✓

1.0b

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

▶

0.5b

(*.f64 x (cbrt.f64 (pow.f64 (exp.f64 (-.f64 (*.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))) 3)))

Compiler

Compiled 14315 to 5966 computations (58.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))) 3))
✓	0.0b	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
✓	0.2b	(*.f64 (log.f64 z) y)
✓	0.5b	(fma.f64 a (+.f64 b z) (*.f64 y t))

series516.0ms (1.5%)

Counts

4 → 176

Calls

4 calls:

344.0ms	(*.f64 (log.f64 z) y)
73.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))) 3))
68.0ms	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
30.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
21×	`exp-sum_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t)))) 3))
7.0ms	(exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (.f64 y t))))
5.0ms	(*.f64 (log.f64 z) y)
1.0ms	(fma.f64 a (+.f64 b z) (*.f64 y t))

simplify288.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

682×	`cancel-sign-sub-inv_binary64`
393×	`associate-r_binary64`
336×	`fma-neg_binary64`
326×	`associate-l_binary64`
229×	`fma-def_binary64`

Counts

267 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	7456
1	835	6905
2	3206	6625
3	5309	6625

prune374.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Error

0.0b

Counts

162 → 3

Alt Table

Status	Error	Program
	37.0b	(.f64 x (cbrt.f64 (pow.f64 (.f64 (exp.f64 (fma.f64 (log.f64 z) y (neg.f64 (.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))))))) (exp.f64 (fma.f64 (neg.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))) (.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))) (.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (.f64 (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t))) (cbrt.f64 (fma.f64 a (+.f64 b z) (.f64 y t)))))))) 3)))
✓	1.0b	(.f64 x (pow.f64 (exp.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b)))))) (cbrt.f64 (fma.f64 y (-.f64 (log.f64 z) t) (*.f64 a (-.f64 (log1p.f64 (neg.f64 z)) b))))))
✓	0.5b	(.f64 x (cbrt.f64 (pow.f64 (exp.f64 (-.f64 (.f64 (log.f64 z) y) (fma.f64 a (+.f64 b z) (*.f64 y t)))) 3)))

Compiler

Compiled 6122 to 1705 computations (72.1% saved)

regimes4.3s (12.8%)

Accuracy

Total 0.3b remaining (91.6%)

Threshold costs 0.3b (91.6%)

Counts

225 → 1

Compiler

Compiled 62840 to 37653 computations (40.1% saved)

simplify8.0ms (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

end158.0ms (0.5%)

Compiler: Compiled 229 to 87 computations (62% saved)

Details

analyze1.8s (5.3%)

sample5.1s (15.3%)

simplify62.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0%)

series2.0s (5.9%)

rewrite40.0ms (0.1%)

simplify438.0ms (1.3%)

prune420.0ms (1.3%)

localize17.0ms (0%)

series11.8s (35.4%)

rewrite35.0ms (0.1%)

simplify1.0s (3.1%)

prune3.8s (11.3%)

localize39.0ms (0.1%)

series102.0ms (0.3%)

rewrite8.0ms (0%)

simplify238.0ms (0.7%)

prune820.0ms (2.5%)

localize32.0ms (0.1%)

series516.0ms (1.5%)

rewrite32.0ms (0.1%)

simplify288.0ms (0.9%)

prune374.0ms (1.1%)

regimes4.3s (12.8%)

simplify8.0ms (0%)

end158.0ms (0.5%)

Profiling