Details

analyze2.7s (22.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
12.5%	87.4%	0.1%	8
31.2%	68.6%	0.1%	9
31.2%	68.6%	0.1%	10
31.2%	68.6%	0.1%	11
40.6%	59.3%	0.1%	12
40.6%	59.3%	0.1%	13
40.6%	59.3%	0.1%	14

Compiler

Compiled 34 to 19 computations (44.1% saved)

sample6.0s (50.9%)

Results

3.1s	2076×	body	1024	valid
1.4s	4580×	body	128	valid
1.0s	1040×	body	512	valid
340.0ms	557×	body	256	valid
13.0ms	3×	body	2048	valid

Compiler

Compiled 101 to 56 computations (44.6% saved)

simplify281.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1350×	`fma-def_binary64`
1306×	`fma-neg_binary64`
889×	`div-sub_binary64`
757×	`associate-/r/_binary64`
558×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	44	50
2	109	50
3	229	50
4	333	50
5	515	50
6	717	50
7	984	50
8	1308	50
9	1633	50
10	1589	50
11	1591	50
12	1623	50
13	1671	50
14	1671	50
15	2103	50
16	2591	50
17	2559	50
18	2615	50
19	2783	50
20	2879	50
21	2927	50
22	3351	50
23	3319	50
24	3319	50
25	2487	50
26	2863	50
27	2591	50
28	2591	50
29	2591	50
30	2591	50
31	2376	50

prune3.0ms (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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Status

Error

Program

▶

0.1b

(fabs.f64 (-.f64 (*.f64 (*.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (*.f64 (*.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 99 to 54 computations (45.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (neg.f64 eh) (tan.f64 t))
✓	0.1b	(*.f64 eh (sin.f64 t))
✓	2.3b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	19.6b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

series100.0ms (0.8%)

Counts

4 → 120

Calls

4 calls:

48.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
25.0ms	(*.f64 (neg.f64 eh) (tan.f64 t))
20.0ms	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))
8.0ms	(*.f64 eh (sin.f64 t))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
4.0ms	(*.f64 eh (sin.f64 t))
4.0ms	(*.f64 (neg.f64 eh) (tan.f64 t))
1.0ms	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
641×	`fma-def_binary64`
349×	`div-sub_binary64`
186×	`fma-neg_binary64`
182×	`distribute-lft-neg-out_binary64`

Counts

205 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	2842
1	468	2661
2	1674	2646
3	4204	2644
4	5113	2644

prune210.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	3	261

Error

0.1b

Counts

261 → 3

Alt Table

Status	Error	Program
	31.4b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 (.f64 eh (sqrt.f64 (sin.f64 t))) (sqrt.f64 (sin.f64 t))) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 9537 to 2081 computations (78.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 eh (sin.f64 t))
✓	1.7b	(log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))))
	2.3b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
	19.6b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

series22.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

22.0ms

(log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-pow_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 17

Calls

1 calls:

2.0ms

(log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

850×	`log-prod_binary64`
664×	`unswap-sqr_binary64`
463×	`fma-def_binary64`
368×	`associate-/l/_binary64`
221×	`associate-/l*_binary64`

Counts

53 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	934
1	60	885
2	94	885
3	139	885
4	192	885
5	302	885
6	533	885
7	1184	885
8	4305	885
9	5269	885

prune173.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	180	3	183

Error

0.1b

Counts

183 → 3

Alt Table

Status	Error	Program
	31.4b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 (.f64 eh (sqrt.f64 (sin.f64 t))) (sqrt.f64 (sin.f64 t))) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 7120 to 1499 computations (78.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.3b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	7.5b	(.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))
	19.6b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))
✓	35.5b	(cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t))))

series46.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))
17.0ms	(cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`pow1_binary64`
53×	`pow-prod-down_binary64`
40×	`pow-plus_binary64`
40×	`pow-prod-up_binary64`
38×	`add-cbrt-cube_binary64`

Counts

2 → 78

Calls

2 calls:

18.0ms	(.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))
14.0ms	(cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (*.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t))))

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

853×	`unswap-sqr_binary64`
502×	`fma-neg_binary64`
448×	`cancel-sign-sub-inv_binary64`
435×	`*-commutative_binary64`
308×	`fma-def_binary64`

Counts

126 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1750
1	276	1458
2	1076	1422
3	2579	1366
4	5124	1366

prune238.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	202	4	206

Error

0.1b

Counts

206 → 4

Alt Table

Status	Error	Program
	31.4b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 (.f64 eh (sqrt.f64 (sin.f64 t))) (sqrt.f64 (sin.f64 t))) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 9646 to 1871 computations (80.6% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.5b	(*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))
	19.6b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))
✓	35.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))))
✓	35.5b	(cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))

series63.0ms (0.5%)

Counts

3 → 52

Calls

3 calls:

30.0ms

(*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))

18.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))))

15.0ms

(cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
16×	`unswap-sqr_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
14×	`unpow-prod-down_binary64`

Counts

3 → 85

Calls

3 calls:

9.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))))

8.0ms

(*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))

4.0ms

(cbrt.f64 (*.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
539×	`log-prod_binary64`
465×	`unswap-sqr_binary64`
450×	`fma-neg_binary64`
274×	`exp-prod_binary64`

Counts

137 → 119

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	2067
1	305	1981
2	1346	1873
3	3214	1867
4	4930	1847
5	5238	1847

prune667.0ms (5.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	351	5	356

Error

0.1b

Counts

356 → 5

Alt Table

Status	Error	Program
	31.4b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 (.f64 eh (sqrt.f64 (sin.f64 t))) (sqrt.f64 (sin.f64 t))) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (log.f64 (exp.f64 (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	23.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 eh eh) eh) (.f64 (.f64 (sin.f64 t) (sin.f64 t)) (sin.f64 t)))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	25.7b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))) (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3)))) (expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 t) 3) (pow.f64 eh 3))))))) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 22396 to 10224 computations (54.3% saved)

regimes639.0ms (5.4%)

Accuracy

Total 0.0b remaining (17.3%)

Threshold costs 0.0b (17.3%)

Counts

78 → 1

Compiler

Compiled 15929 to 9828 computations (38.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
15×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	52
1	42	52
2	71	52
3	99	52
4	120	52
5	131	52
6	133	52
7	133	52

end177.0ms (1.5%)

Compiler: Compiled 305 to 187 computations (38.7% saved)

Details

analyze2.7s (22.3%)

sample6.0s (50.9%)

simplify281.0ms (2.4%)

prune3.0ms (0%)

localize22.0ms (0.2%)

series100.0ms (0.8%)

rewrite17.0ms (0.1%)

simplify107.0ms (0.9%)

prune210.0ms (1.8%)

localize24.0ms (0.2%)

series22.0ms (0.2%)

rewrite3.0ms (0%)

simplify87.0ms (0.7%)

prune173.0ms (1.5%)

localize29.0ms (0.2%)

series46.0ms (0.4%)

rewrite43.0ms (0.4%)

simplify70.0ms (0.6%)

prune238.0ms (2%)

localize31.0ms (0.3%)

series63.0ms (0.5%)

rewrite25.0ms (0.2%)

simplify106.0ms (0.9%)

prune667.0ms (5.6%)

regimes639.0ms (5.4%)

simplify5.0ms (0%)

end177.0ms (1.5%)

Profiling