Details

analyze1.3s (13.9%)

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
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample174.0ms (1.8%)

Algorithm

1×

intervals

Results

104.0ms	62×	body	2048	valid
42.0ms	93×	body	1024	valid
12.0ms	53×	body	512	valid
3.0ms	25×	body	256	valid
2.0ms	22×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify249.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	990	14
1	990	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

Merged error: 31.2b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_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×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

3 calls:

10.0ms	(/.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))

series290.0ms (3%)

Counts

3 → 9

Calls

3 calls:

123.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
102.0ms	(-.f64 x (tan.f64 x))
65.0ms	(-.f64 x (sin.f64 x))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4881	1847
1	4881	1847

prune161.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Merged error: 0.0b

Counts

94 → 5

Compiler

Compiled 2927 to 1118 computations (61.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series327.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(-.f64 x (tan.f64 x))
97.0ms	(-.f64 x (tan.f64 x))
88.0ms	(-.f64 x (tan.f64 x))
42.0ms	(-.f64 x (sin.f64 x))

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5123	858

prune67.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	76	5	81

Merged error: 0.0b

Counts

81 → 5

Compiler

Compiled 2092 to 354 computations (83.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
13.6b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 60

Calls

3 calls:

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

series147.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

60.0ms	(*.f64 27/2800 (pow.f64 x 4))
53.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
34.0ms	(.f64 (.f64 x x) 9/40)

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5523	873

prune88.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	69	5	74

Merged error: 0b

Counts

74 → 5

Compiler

Compiled 1447 to 1030 computations (28.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
13.6b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `associate--l+_binary64`
3×	`pow-prod-down_binary64` `diff-log_binary64`
2×	`sub-neg_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

3 → 62

Calls

3 calls:

11.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
6.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))

series153.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(*.f64 27/2800 (pow.f64 x 4))
51.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
41.0ms	(.f64 (.f64 x x) 9/40)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5345	894

prune68.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Merged error: 0b

Counts

76 → 5

Compiler

Compiled 1209 to 873 computations (27.8% saved)

regimes43.0ms (0.4%)

Compiler: Compiled 190 to 112 computations (41.1% saved)

bsearch45.0ms (0.5%)

Steps

Iters	Range		Point
8	0.00041078065762387996	1.6782813896091193	0.029551278348766707
10	-2111.3188392448023	-2.1543716108783144e-07	-0.023947268971373566

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	76	59
1	76	59

end0.0ms (0%)

sample6.1s (63%)

Algorithm

1×

intervals

Results

3.9s	2027×	body	2048	valid
1.2s	3049×	body	1024	valid
292.0ms	1451×	body	512	valid
148.0ms	120×	body	4096	valid
113.0ms	753×	body	256	valid
53.0ms	600×	body	128	valid

Compiler

Compiled 134 to 79 computations (41% saved)

Details

analyze1.3s (13.9%)

sample174.0ms (1.8%)

simplify249.0ms (2.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite29.0ms (0.3%)

series290.0ms (3%)

simplify73.0ms (0.8%)

prune161.0ms (1.7%)

localize14.0ms (0.1%)

rewrite23.0ms (0.2%)

series327.0ms (3.4%)

simplify79.0ms (0.8%)

prune67.0ms (0.7%)

localize8.0ms (0.1%)

rewrite25.0ms (0.3%)

series147.0ms (1.5%)

simplify59.0ms (0.6%)

prune88.0ms (0.9%)

localize9.0ms (0.1%)

rewrite28.0ms (0.3%)

series153.0ms (1.6%)

simplify57.0ms (0.6%)

prune68.0ms (0.7%)

regimes43.0ms (0.4%)

bsearch45.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (63%)

Profiling