Details

analyze1.9s (13.1%)

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%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.1s (63.7%)

Results

5.1s	2020×	body	2048	valid
2.4s	3124×	body	1024	valid
731.0ms	1561×	body	512	valid
410.0ms	702×	body	128	valid
202.0ms	743×	body	256	valid
146.0ms	106×	body	4096	valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

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

30.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.5b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.5b	(-.f64 x (sin.f64 x))
✓	1.7b	(-.f64 x (tan.f64 x))

series19.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune103.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	3	154

Error

0.0b

Counts

154 → 3

Alt Table

Status	Error	Program
▶	31.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	31.0b	(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x)))) (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) x))
	32.6b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 3245 to 921 computations (71.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	1.5b	(-.f64 x (sin.f64 x))
	1.7b	(-.f64 x (tan.f64 x))

series13.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

rewrite89.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

237×	`*-un-lft-identity_binary64`
199×	`add-sqr-sqrt_binary64`
186×	`sqrt-prod_binary64`
160×	`times-frac_binary64`
76×	`distribute-lft-out--_binary64`

Counts

1 → 173

Calls

1 calls:

35.0ms

(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

simplify279.0ms (2%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
442×	`times-frac_binary64`
398×	`associate-/l*_binary64`
217×	`associate-/r*_binary64`
172×	`associate-l_binary64`

Counts

185 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	5563
1	495	5319
2	1617	5189
3	4800	5185
4	5354	5185

prune279.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	488	3	491

Error

0.0b

Counts

491 → 3

Alt Table

Status	Error	Program
	32.6b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
✓	31.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	31.0b	(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x)))) (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) x))

Compiler

Compiled 15848 to 2733 computations (82.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 x) (cos.f64 x))
✓	0.3b	(pow.f64 (cos.f64 x) 2)
✓	2.0b	(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	15.4b	(/.f64 (sin.f64 x) (*.f64 x x))

series55.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

38.0ms	(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
9.0ms	(/.f64 (sin.f64 x) (cos.f64 x))
4.0ms	(pow.f64 (cos.f64 x) 2)
4.0ms	(/.f64 (sin.f64 x) (*.f64 x x))

rewrite153.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

635×	`times-frac_binary64`
462×	`add-sqr-sqrt_binary64`
446×	`*-un-lft-identity_binary64`
433×	`add-cube-cbrt_binary64`
364×	`prod-diff_binary64`

Counts

4 → 511

Calls

4 calls:

29.0ms	(-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))
4.0ms	(/.f64 (sin.f64 x) (*.f64 x x))
3.0ms	(/.f64 (sin.f64 x) (cos.f64 x))
2.0ms	(pow.f64 (cos.f64 x) 2)

simplify585.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-neg_binary64`
417×	`associate-/l/_binary64`
300×	`fma-udef_binary64`
235×	`cancel-sign-sub-inv_binary64`
224×	`unsub-neg_binary64`

Counts

535 → 611

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	610	29223
1	1202	15539
2	2164	11151
3	4370	11151
4	4825	11151

prune508.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	611	0	611
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	611	3	614

Error

0.0b

Counts

614 → 3

Alt Table

Status	Error	Program
▶	32.6b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
✓	31.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	31.0b	(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x)))) (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) x))

Compiler

Compiled 42475 to 10426 computations (75.5% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
✓	0.0b	(fma.f64 (pow.f64 x 4) -27/2800 -1/2)
✓	19.8b	(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

series15.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

7.0ms

(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

4.0ms

(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))

3.0ms

(fma.f64 (pow.f64 x 4) -27/2800 -1/2)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 30

Calls

3 calls:

0.0ms

(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

0.0ms

(fma.f64 (pow.f64 x 4) -27/2800 -1/2)

0.0ms

(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-def_binary64`
493×	`fma-neg_binary64`
413×	`exp-prod_binary64`
318×	`unsub-neg_binary64`
301×	`exp-sum_binary64`

Counts

66 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	1087
1	110	942
2	241	942
3	1018	942
4	2657	942
5	4666	942
6	5018	942

prune53.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
	32.6b	(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 (fma.f64 9/40 (*.f64 x x) -1/2)))
✓	31.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))) (sqrt.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	31.0b	(-.f64 (+.f64 (+.f64 1 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x)))) (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) x))

Compiler

Compiled 1394 to 1002 computations (28.1% saved)

regimes652.0ms (4.6%)

Accuracy

Total 0.1b remaining (58.3%)

Threshold costs 0.1b (58.3%)

Counts

196 → 3

Compiler

Compiled 9160 to 4927 computations (46.2% saved)

bsearch57.0ms (0.4%)

Steps

Iters	Range		Point
7	0.01943739513230401	1.9433347259186247	0.09177400000757278
10	-2076402.2840280668	-2.170070029474248e-5	-2.7247982106534647

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	102
1	60	102
2	71	102
3	77	102
4	80	102
5	77	102

end95.0ms (0.7%)

Compiler: Compiled 211 to 119 computations (43.6% saved)

Details

analyze1.9s (13.1%)

sample9.1s (63.7%)

simplify87.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

series19.0ms (0.1%)

rewrite24.0ms (0.2%)

simplify106.0ms (0.7%)

prune103.0ms (0.7%)

localize9.0ms (0.1%)

series13.0ms (0.1%)

rewrite89.0ms (0.6%)

simplify279.0ms (2%)

prune279.0ms (2%)

localize20.0ms (0.1%)

series55.0ms (0.4%)

rewrite153.0ms (1.1%)

simplify585.0ms (4.1%)

prune508.0ms (3.6%)

localize11.0ms (0.1%)

series15.0ms (0.1%)

rewrite3.0ms (0%)

simplify76.0ms (0.5%)

prune53.0ms (0.4%)

regimes652.0ms (4.6%)

bsearch57.0ms (0.4%)

simplify6.0ms (0%)

end95.0ms (0.7%)

Profiling