Details

analyze1.8s (13.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14
0	1	1
1	1	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
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample162.0ms (1.2%)

Algorithm

1×

intervals

Results

100.0ms	71×	body	2048	valid
25.0ms	80×	body	1024	valid
9.0ms	51×	body	512	valid
4.0ms	28×	body	256	valid
4.0ms	3×	body	4096	valid
2.0ms	23×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune4.0ms (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

31.8b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.7b	(-.f64 x (tan.f64 x))
1.7b	(-.f64 x (sin.f64 x))

rewrite113.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

30.6b

Rules

45×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

3 → 84

Calls

3 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
9.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 1513 to 300 computations (80.2% saved)

series274.0ms (2.1%)

Error

0.0b

Counts

3 → 20

Calls

3 calls:

118.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
67.0ms	(-.f64 x (tan.f64 x))
43.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 768 to 442 computations (42.4% saved)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5388	2053

prune105.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	3	105

Error

Counts

105 → 3

Compiler

Compiled 1800 to 386 computations (78.6% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

0.1b	(.f64 9/40 (.f64 x x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `associate-l_binary64`
2×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
1×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

1 → 19

Calls

1 calls:

6.0ms

(*.f64 9/40 (*.f64 x x))

Compiler

Compiled 231 to 151 computations (34.6% saved)

series29.0ms (0.2%)

Error

Counts

1 → 3

Calls

1 calls:

26.0ms

(*.f64 9/40 (*.f64 x x))

Compiler

Compiled 63 to 61 computations (3.2% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4846	180
1	4846	180

prune17.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

Counts

25 → 3

Compiler

Compiled 286 to 188 computations (34.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
1.7b	(-.f64 x (tan.f64 x))
1.7b	(-.f64 x (sin.f64 x))

rewrite298.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

218×	`times-frac_binary64`
202×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
94×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `div-exp_binary64` `associate-/l*_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64` `div-sub_binary64`

Counts

4 → 232

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
9.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 5463 to 1537 computations (71.9% saved)

series368.0ms (2.8%)

Error

Counts

4 → 30

Calls

4 calls:

149.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
95.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
53.0ms	(-.f64 x (tan.f64 x))
37.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1318 to 801 computations (39.2% saved)

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5144	6725

prune231.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	262	3	265

Error

Counts

265 → 3

Compiler

Compiled 5408 to 1237 computations (77.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
16.1b	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))
16.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))

rewrite425.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

86×	`add-exp-log_binary64`
36×	`prod-exp_binary64`
30×	`div-exp_binary64`
22×	`add-cbrt-cube_binary64`
18×	`pow-to-exp_binary64` `pow-exp_binary64` `unpow-prod-down_binary64`
16×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `associate-/l_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `sqr-pow_binary64` `pow-unpow_binary64`
4×	`add-log-exp_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64` `pow-pow_binary64`

Counts

4 → 126

Calls

4 calls:

11.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))
9.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))
5.0ms	(pow.f64 (sin.f64 x) 2)
4.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 8666 to 3396 computations (60.8% saved)

series315.0ms (2.4%)

Error

Counts

4 → 13

Calls

4 calls:

130.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))
83.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))
37.0ms	(pow.f64 (sin.f64 x) 2)
33.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 2324 to 1114 computations (52.1% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5033	2067

prune385.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

Counts

142 → 3

Compiler

Compiled 8919 to 3326 computations (62.7% saved)

regimes138.0ms (1.1%)

Accuracy

Total 0.5b remaining (92.2%)

Threshold costs 0.5b (92.2%)

Compiler

Compiled 833 to 504 computations (39.5% saved)

bsearch52.0ms (0.4%)

Steps

Iters	Range		Point
9	1.6130476882321248e-06	31.96947741202035	0.004331643272607194
11	-1.1500682954987618e+19	-1.800146080632152e-07	-2.619158073142093

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	40
1	41	40

end0.0ms (0%)

sample7.8s (59.8%)

Algorithm

1×

intervals

Results

5.1s	2032×	body	2048	valid
1.3s	2929×	body	1024	valid
361.0ms	1524×	body	512	valid
129.0ms	772×	body	256	valid
124.0ms	103×	body	4096	valid
60.0ms	640×	body	128	valid

Compiler

Compiled 429 to 262 computations (38.9% saved)

Details

analyze1.8s (13.8%)

sample162.0ms (1.2%)

simplify98.0ms (0.7%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite113.0ms (0.9%)

series274.0ms (2.1%)

simplify83.0ms (0.6%)

prune105.0ms (0.8%)

localize6.0ms (0%)

rewrite22.0ms (0.2%)

series29.0ms (0.2%)

simplify59.0ms (0.5%)

prune17.0ms (0.1%)

localize8.0ms (0.1%)

rewrite298.0ms (2.3%)

series368.0ms (2.8%)

simplify130.0ms (1%)

prune231.0ms (1.8%)

localize28.0ms (0.2%)

rewrite425.0ms (3.3%)

series315.0ms (2.4%)

simplify87.0ms (0.7%)

prune385.0ms (2.9%)

regimes138.0ms (1.1%)

bsearch52.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.8s (59.8%)

Profiling