Details

analyze1.5s (15.9%)

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

Symmetry

Compiler

Compiled 10 to 7 computations (30% saved)

sample159.0ms (1.6%)

Algorithm

1×

intervals

Results

91.0ms	50×	body	2048	valid
40.0ms	107×	body	1024	valid
8.0ms	43×	body	512	valid
3.0ms	25×	body	256	valid
3.0ms	3×	body	4096	valid
2.0ms	28×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

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

30.2b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite97.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

29.2b

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:

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

Compiler

Compiled 1513 to 300 computations (80.2% saved)

series242.0ms (2.5%)

Error

0.0b

Counts

3 → 23

Calls

3 calls:

116.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
59.0ms	(-.f64 x (tan.f64 x))
39.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 878 to 528 computations (39.9% saved)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4957	2110
1	4957	2110

prune80.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

Counts

108 → 4

Compiler

Compiled 1830 to 404 computations (77.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))
2.1b	(-.f64 x (sin.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
12×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
8×	`add-cube-cbrt_binary64`
4×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`

Counts

4 → 64

Calls

4 calls:

4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 2456 to 327 computations (86.7% saved)

series172.0ms (1.8%)

Error

Counts

4 → 24

Calls

4 calls:

54.0ms	(-.f64 x (tan.f64 x))
35.0ms	(-.f64 x (sin.f64 x))
32.0ms	(-.f64 x (sin.f64 x))
28.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 2009 to 600 computations (70.1% saved)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5116	838

prune88.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	88	4	92

Error

Counts

92 → 4

Compiler

Compiled 3155 to 368 computations (88.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.3b	(.f64 9/40 (.f64 x x))
17.1b	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
6×	`prod-exp_binary64` `associate-l_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`cancel-sign-sub-inv_binary64` `pow-prod-down_binary64`
2×	`diff-log_binary64` `*-commutative_binary64` `sqr-pow_binary64`
1×	`sum-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `associate--r+_binary64` `pow-to-exp_binary64` `pow-exp_binary64`

Counts

3 → 60

Calls

3 calls:

8.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
5.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 1235 to 905 computations (26.7% saved)

series116.0ms (1.2%)

Error

Counts

3 → 11

Calls

3 calls:

44.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
36.0ms	(*.f64 27/2800 (pow.f64 x 4))
29.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 331 to 289 computations (12.7% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4889	858
1	4889	858

prune66.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	71	4	75

Error

Counts

75 → 4

Compiler

Compiled 1188 to 864 computations (27.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite128.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

43×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64`
19×	`pow1_binary64`
15×	`add-cube-cbrt_binary64`
12×	`sqrt-div_binary64` `swap-sqr_binary64`
10×	`add-log-exp_binary64`
9×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
8×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-l_binary64` `associate-r_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`frac-times_binary64` `unswap-sqr_binary64`
3×	`diff-log_binary64` `sub-neg_binary64` `pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64` `associate-l/_binary64` `associate-r/_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `*-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 2756 to 502 computations (81.8% saved)

series141.0ms (1.4%)

Error

Counts

4 → 20

Calls

4 calls:

48.0ms	(-.f64 x (tan.f64 x))
29.0ms	(*.f64 (sqrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (-.f64 x (sin.f64 x))))
26.0ms	(-.f64 x (sin.f64 x))
26.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 790 to 377 computations (52.3% saved)

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4995	1435
1	4995	1435

prune87.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	134	4	138

Error

Counts

138 → 4

Compiler

Compiled 2414 to 430 computations (82.2% saved)

regimes132.0ms (1.4%)

Accuracy

Total 0.0b remaining (54.7%)

Threshold costs 0.0b (54.7%)

Compiler

Compiled 871 to 521 computations (40.2% saved)

bsearch54.0ms (0.6%)

Steps

Iters	Range		Point
9	5.75105143177422e-05	26.7272813147975	0.03361492514081578
9	-331001.63089080155	-0.0005244387801165087	-0.03085132230042529

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	63
1	110	63

Removed

()

end0.0ms (0%)

sample6.0s (61.8%)

Algorithm

1×

intervals

Results

3.7s	1871×	body	2048	valid
1.0s	3146×	body	1024	valid
272.0ms	1510×	body	512	valid
108.0ms	111×	body	4096	valid
96.0ms	743×	body	256	valid
46.0ms	619×	body	128	valid

Compiler

Compiled 445 to 272 computations (38.9% saved)

Details

analyze1.5s (15.9%)

sample159.0ms (1.6%)

simplify78.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.2%)

rewrite97.0ms (1%)

series242.0ms (2.5%)

simplify68.0ms (0.7%)

prune80.0ms (0.8%)

localize12.0ms (0.1%)

rewrite90.0ms (0.9%)

series172.0ms (1.8%)

simplify62.0ms (0.6%)

prune88.0ms (0.9%)

localize8.0ms (0.1%)

rewrite90.0ms (0.9%)

series116.0ms (1.2%)

simplify89.0ms (0.9%)

prune66.0ms (0.7%)

localize9.0ms (0.1%)

rewrite128.0ms (1.3%)

series141.0ms (1.4%)

simplify75.0ms (0.8%)

prune87.0ms (0.9%)

regimes132.0ms (1.4%)

bsearch54.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.0s (61.8%)

Profiling