Details

analyze348.0ms (7.6%)

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 43 to 31 computations (27.9% saved)

sample1.5s (32%)

Results

1.2s	7931×	body	128	valid
122.0ms	860×	body	128	invalid
85.0ms	325×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 60 to 42 computations (30% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	30.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series125.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
33.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
27.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite118.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

4 → 156

Calls

4 calls:

114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
114.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
114.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	337	62
2	4158	62
3	4987	62
4	4850	62

prune142.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	248	5	253

Error

0.8b

Counts

253 → 5

Alt Table

Status	Error	Program
	5.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	30.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	30.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))
	29.2b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
▶	5.8b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))

Compiler

Compiled 6374 to 3830 computations (39.9% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 3))

series202.0ms (4.4%)

Counts

4 → 0

Calls

4 calls:

91.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
79.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
19.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
13.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))

rewrite117.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

318×	`log1p-udef_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`
186×	`add-sqr-sqrt_binary64`
179×	`add-log-exp_binary64`

Counts

4 → 116

Calls

4 calls:

114.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
114.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
114.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
114.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	52
1	417	52
2	4553	52
3	5101	52

prune248.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Error

0.7b

Counts

121 → 7

Alt Table

Status	Error	Program
▶	5.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	30.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	7.2b	(neg.f64 (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	29.2b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
	6.3b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	5.8b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	30.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))

Compiler

Compiled 5812 to 4113 computations (29.2% saved)

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

series192.0ms (4.2%)

Counts

4 → 0

Calls

4 calls:

84.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
68.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
19.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))

rewrite72.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

320×	`log1p-udef_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
194×	`add-sqr-sqrt_binary64`
191×	`add-cbrt-cube_binary64`

Counts

4 → 112

Calls

4 calls:

69.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
69.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
69.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
69.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	40
1	457	40
2	4321	40
3	4956	40

prune229.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	111	8	119

Error

0.7b

Counts

119 → 8

Alt Table

Status	Error	Program
✓	5.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	30.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	7.2b	(neg.f64 (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	29.2b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
▶	6.3b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	5.8b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	7.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))))) (*.f64 2 a))
	30.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))

Compiler

Compiled 6790 to 4736 computations (30.3% saved)

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
✓	27.5b	(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))

series217.0ms (4.7%)

Counts

4 → 36

Calls

4 calls:

94.0ms	(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))
91.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
18.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
13.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))

rewrite78.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`expm1-udef_binary64`
272×	`log1p-udef_binary64`
256×	`log-pow_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Counts

4 → 142

Calls

4 calls:

74.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
74.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 2))
74.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
74.0ms	(log.f64 (exp.f64 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	359	52
2	3723	52
3	4889	52

prune328.0ms (7.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	178	8	186

Error

0.7b

Counts

186 → 8

Alt Table

Status	Error	Program
✓	5.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	30.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	7.2b	(neg.f64 (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5))))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	29.2b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	6.3b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	5.8b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
	7.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))))) (*.f64 2 a))
	30.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))

Compiler

Compiled 8596 to 6227 computations (27.6% saved)

regimes279.0ms (6.1%)

Accuracy

Total 4.5b remaining (84.2%)

Threshold costs 0b (0%)

Counts

40 → 2

Compiler

Compiled 6664 to 4930 computations (26% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 20 to 14 computations (30% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

33×	`*-commutative_binary64`
30×	`+-commutative_binary64`
25×	`sub-neg_binary64`
23×	`neg-sub0_binary64`
23×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	135
1	85	131
2	124	131
3	162	131
4	198	131
5	230	131
6	248	131
7	258	131
8	261	131
9	258	131

end308.0ms (6.7%)

Compiler: Compiled 506 to 358 computations (29.2% saved)

Iter	Nodes	Cost
0	52	135
1	85	131
2	124	131
3	162	131
4	198	131
5	230	131
6	248	131
7	258	131
8	261	131
9	258	131

Iter	Nodes	Cost
0	52	135
1	85	131
2	124	131
3	162	131
4	198	131
5	230	131
6	248	131
7	258	131
8	261	131
9	258	131

Details

analyze348.0ms (7.6%)

sample1.5s (32%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series125.0ms (2.7%)

rewrite118.0ms (2.6%)

prune142.0ms (3.1%)

localize25.0ms (0.5%)

series202.0ms (4.4%)

rewrite117.0ms (2.6%)

prune248.0ms (5.4%)

localize33.0ms (0.7%)

series192.0ms (4.2%)

rewrite72.0ms (1.6%)

prune229.0ms (5%)

localize28.0ms (0.6%)

series217.0ms (4.7%)

rewrite78.0ms (1.7%)

prune328.0ms (7.2%)

regimes279.0ms (6.1%)

bsearch3.0ms (0.1%)

simplify9.0ms (0.2%)

end308.0ms (6.7%)

Profiling

Iter	Nodes	Cost
0	52	135
1	85	131
2	124	131
3	162	131
4	198	131
5	230	131
6	248	131
7	258	131
8	261	131
9	258	131