Details

analyze2.1s (14.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0.8%	99.2%	0%	8
1.2%	98.8%	0%	9
1.6%	98.4%	0%	10
1.7%	98.3%	0%	11
1.7%	98.2%	0%	12
1.8%	98.2%	0%	13
1.8%	98.1%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample11.0s (73.1%)

Results

4.7s	1540×	body	8192	exit
3.1s	4132×	body	1024	valid
1.1s	1666×	body	1024	invalid
941.0ms	2067×	body	512	valid
344.0ms	812×	body	512	invalid
303.0ms	998×	body	256	valid
161.0ms	171×	body	2048	valid
152.0ms	888×	body	128	valid
121.0ms	448×	body	256	invalid
72.0ms	408×	body	128	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
493×	`fma-neg_binary64`
430×	`associate-/l*_binary64`
379×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	25	15
3	36	15
4	59	15
5	103	15
6	204	15
7	435	15
8	703	15
9	1995	15
10	2934	15
11	3478	15
12	4158	15
13	4980	15
14	4913	15

prune3.0ms (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

60.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.1b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series13.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

8.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
3.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 53

Calls

3 calls:

3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

599×	`cancel-sign-sub-inv_binary64`
541×	`fma-def_binary64`
463×	`times-frac_binary64`
381×	`div-sub_binary64`
282×	`fma-neg_binary64`

Counts

61 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1190
1	212	1105
2	477	1069
3	1265	1049
4	3482	1048
5	4641	1048
6	5116	1048

prune51.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Error

60.1b

Counts

74 → 3

Alt Table

Status	Error	Program
▶	60.1b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
	60.1b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.8b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1273 to 353 computations (72.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
	0.0b	(sqrt.f64 (cos.f64 x))
	4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series34.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

25.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
9.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

4.0ms	(pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)
4.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))

simplify115.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

596×	`times-frac_binary64`
400×	`associate-/l*_binary64`
398×	`log-div_binary64`
326×	`unswap-sqr_binary64`
300×	`fma-def_binary64`

Counts

116 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	3353
1	370	3026
2	1185	2860
3	4553	2845
4	5398	2845

prune107.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Error

60.1b

Counts

143 → 3

Alt Table

Status	Error	Program
✓	60.1b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
▶	60.1b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.8b	(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))

Compiler

Compiled 3031 to 1029 computations (66.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.0b	(log1p.f64 (sqrt.f64 (cos.f64 x)))
✓	0.1b	(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
✓	47.8b	(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))

series230.0ms (1.5%)

Counts

3 → 36

Calls

3 calls:

225.0ms	(log1p.f64 (sqrt.f64 (cos.f64 x)))
3.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 31

Calls

3 calls:

1.0ms	(log1p.f64 (sqrt.f64 (cos.f64 x)))
0.0ms	(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-neg-in_binary64`
590×	`distribute-lft-neg-in_binary64`
440×	`fma-def_binary64`
419×	`associate-l_binary64`
400×	`cancel-sign-sub-inv_binary64`

Counts

67 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	705
1	131	631
2	277	624
3	784	620
4	2767	620
5	4537	620
6	5129	620

prune78.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	85	4	89

Error

58.0b

Counts

89 → 4

Alt Table

Status	Error	Program
▶	58.4b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	58.4b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.8b	(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))

Compiler

Compiled 1491 to 606 computations (59.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))
✓	0.8b	(sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
✓	0.9b	(*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))
✓	47.8b	(fmod.f64 (exp.f64 x) (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))))

series449.0ms (3%)

Counts

4 → 48

Calls

4 calls:

224.0ms	(sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
220.0ms	(*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))
3.0ms	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))
2.0ms	(fmod.f64 (exp.f64 x) (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))
1.0ms	(sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
0.0ms	(expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))
0.0ms	(fmod.f64 (exp.f64 x) (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))))

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

470×	`fma-neg_binary64`
368×	`fma-def_binary64`
290×	`distribute-rgt-neg-in_binary64`
274×	`distribute-lft-neg-in_binary64`
272×	`associate-l_binary64`

Counts

136 → 137

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1962
1	296	1576
2	772	1512
3	2578	1482
4	4793	1462
5	4972	1462
6	4995	1462
7	4962	1462

prune109.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Error

33.4b

Counts

168 → 5

Alt Table

Status	Error	Program
	34.0b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (cbrt.f64 (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))))) (cbrt.f64 (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))
	58.4b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) 4) (cbrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	58.4b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))) (expm1.f64 (.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))
	60.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.8b	(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))

Compiler

Compiled 4070 to 1429 computations (64.9% saved)

regimes147.0ms (1%)

Accuracy

Total 0.6b remaining (1.6%)

Threshold costs 0.6b (1.6%)

Counts

81 → 1

Compiler

Compiled 2636 to 1676 computations (36.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	86
1	15	86
2	15	86

end103.0ms (0.7%)

Compiler: Compiled 236 to 83 computations (64.8% saved)

Details

analyze2.1s (14.1%)

sample11.0s (73.1%)

simplify84.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series13.0ms (0.1%)

rewrite7.0ms (0%)

simplify95.0ms (0.6%)

prune51.0ms (0.3%)

localize10.0ms (0.1%)

series34.0ms (0.2%)

rewrite15.0ms (0.1%)

simplify115.0ms (0.8%)

prune107.0ms (0.7%)

localize11.0ms (0.1%)

series230.0ms (1.5%)

rewrite3.0ms (0%)

simplify87.0ms (0.6%)

prune78.0ms (0.5%)

localize13.0ms (0.1%)

series449.0ms (3%)

rewrite12.0ms (0.1%)

simplify138.0ms (0.9%)

prune109.0ms (0.7%)

regimes147.0ms (1%)

simplify3.0ms (0%)

end103.0ms (0.7%)

Profiling