Details

analyze1.2s (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample2.9s (28.7%)

Results

1.6s	10368×	body	128	invalid
1.3s	8256×	body	128	valid

Compiler

Compiled 48 to 40 computations (16.7% saved)

preprocess54.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1584×	`associate-/l/_binary64`
504×	`associate-l_binary64`
420×	`associate-r_binary64`
375×	`associate-/l*_binary64`
285×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	182
1	174	161
2	658	140
3	3018	140
4	4048	140
5	4048	140
0	4	4
1	4	4

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort y z)

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify35.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

854×	`associate-/l/_binary64`
849×	`associate-l_binary64`
777×	`associate-/r/_binary64`
378×	`*-commutative_binary64`
330×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	123	20
3	502	20
4	2173	20
5	3870	20
6	3929	20
7	3929	20

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

Compiler

Compiled 82 to 65 computations (20.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (/.f64 x (.f64 y 27)))
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	3.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	6.0b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series80.0ms (0.8%)

Counts

4 → 144

Calls

39 calls:

7.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))	z	-inf
4.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	y	inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	-inf
3.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))	x	0

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
179×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	73
1	398	61

Stop Event

1×	node limit

Counts

4 → 126

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

112×	`associate-/l*_binary64`
61×	`associate-*r/_binary64`
60×	`associate-*l/_binary64`
39×	`associate-/r/_binary64`
38×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	2028
1	32	2028
2	82	2028
3	212	2028
4	368	2028
5	503	2028
6	513	2028

Stop Event

1×

saturated

Counts

270 → 134

prune117.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	132	3	135

Error

0.0b

Counts

135 → 3

Alt Table

Status	Error	Program
	1.7b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
▶	0.8b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))) 1)
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

Compiler

Compiled 2828 to 1960 computations (30.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 t) (/.f64 3 z))
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))
✓	8.7b	(.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))

series1.7s (16.6%)

Counts

4 → 144

Calls

42 calls:

141.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	x	-inf
140.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	t	inf
137.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	y	-inf
134.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	t	-inf
134.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))	z	inf

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`prod-diff_binary64`
183×	`add-sqr-sqrt_binary64`
173×	`expm1-log1p-u_binary64`
172×	`log1p-expm1-u_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	75
1	370	75
2	4746	75

Stop Event

1×	node limit

Counts

4 → 86

simplify141.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

233×	`associate-/l*_binary64`
156×	`times-frac_binary64`
128×	`associate-*l/_binary64`
126×	`associate-/l/_binary64`
118×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	2700
1	41	2664
2	92	2664
3	264	2664
4	594	2664
5	1011	2664
6	1287	2664
7	1318	2664
8	1319	2664
9	1319	2664

Stop Event

1×

saturated

Counts

230 → 94

prune86.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
	1.7b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
▶	0.0b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)

Status

Error

Program

1.7b

(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (*.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))

▶

0.0b

(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))) 1)

Compiler

Compiled 2121 to 1514 computations (28.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	2.9b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	6.6b	(/.f64 x (*.f64 y z))

series1.7s (17.4%)

Counts

4 → 48

Calls

45 calls:

159.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	x	inf
147.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	x	-inf
144.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	t	-inf
143.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	y	inf
138.0ms	(log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))	t	inf

rewrite67.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
203×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	312	61
2	3942	61

Stop Event

1×	node limit

Counts

4 → 98

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

107×	`associate-/l*_binary64`
60×	`associate-*r/_binary64`
57×	`associate-*l/_binary64`
47×	`associate-/l/_binary64`
44×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	1056
1	31	1056
2	66	1056
3	173	1056
4	319	1056
5	496	1056
6	519	1056

Stop Event

1×

saturated

Counts

146 → 100

prune67.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Error

Counts

102 → 2

Alt Table

Status	Error	Program
▶	1.7b	(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))
✓	0.0b	(-.f64 (exp.f64 (log1p.f64 (.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))))))) 1)

Status

Error

Program

▶

1.7b

(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (*.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))

✓

0.0b

(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))) 1)

Compiler

Compiled 2163 to 1367 computations (36.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 x y) 54)
	0.3b	(*.f64 (sqrt.f64 t) (/.f64 3 z))
✓	1.0b	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))
	8.7b	(.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))

series695.0ms (7%)

Counts

2 → 72

Calls

18 calls:

62.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))	z	-inf
59.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))	t	inf
59.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))	z	inf
58.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))	x	inf
58.0ms	(pow.f64 (exp.f64 1/3) (acos.f64 (.f64 (.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54))))	y	-inf

rewrite64.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

327×	`log1p-udef_binary64`
185×	`add-sqr-sqrt_binary64`
174×	`add-log-exp_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	374	32
2	4814	32

Stop Event

1×	node limit

Counts

2 → 47

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
341×	`associate-/l*_binary64`
339×	`associate-*l/_binary64`
298×	`sqr-pow_binary64`
294×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	1224
1	32	1224
2	75	1176
3	195	1176
4	367	1176
5	602	1176
6	789	1176
7	1378	1176
8	2716	1176
9	3677	1176
10	3992	1176
11	4388	1176

Stop Event

1×	node limit

Counts

119 → 50

prune58.0ms (0.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	111	2	113

Error

Counts

113 → 2

Alt Table

Status

Error

Program

✓

1.7b

(log.f64 (pow.f64 (exp.f64 1/3) (acos.f64 (*.f64 (*.f64 (sqrt.f64 t) (/.f64 3 z)) (/.f64 (/.f64 x y) 54)))))

✓

0.0b

(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))) 1)

Compiler

Compiled 2290 to 1562 computations (31.8% saved)

regimes626.0ms (6.3%)

Accuracy

Total 0.3b remaining (92.6%)

Threshold costs 0.3b (92.6%)

Counts

46 → 1

Compiler

Compiled 12814 to 10344 computations (19.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	27	27
2	28	27

Stop Event

1×

saturated

end67.0ms (0.7%)

Stop Event

1×

done

Remove

(sort y z)

Compiler

Compiled 126 to 102 computations (19% saved)

Details

analyze1.2s (11.7%)

sample2.9s (28.7%)

preprocess54.0ms (0.5%)

simplify35.0ms (0.4%)

prune9.0ms (0.1%)

localize12.0ms (0.1%)

series80.0ms (0.8%)

rewrite42.0ms (0.4%)

simplify66.0ms (0.7%)

prune117.0ms (1.2%)

localize15.0ms (0.1%)

series1.7s (16.6%)

rewrite80.0ms (0.8%)

simplify141.0ms (1.4%)

prune86.0ms (0.9%)

localize14.0ms (0.1%)

series1.7s (17.4%)

rewrite67.0ms (0.7%)

simplify40.0ms (0.4%)

prune67.0ms (0.7%)

localize16.0ms (0.2%)

series695.0ms (7%)

rewrite64.0ms (0.6%)

simplify96.0ms (1%)

prune58.0ms (0.6%)

regimes626.0ms (6.3%)

simplify3.0ms (0%)

end67.0ms (0.7%)

Profiling