Details

analyze1.4s (13.8%)

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)

sample206.0ms (2.1%)

Algorithm

1×

intervals

Results

130.0ms	61×	body	2048	valid
42.0ms	113×	body	1024	valid
10.0ms	8×	body	4096	valid
8.0ms	37×	body	512	valid
3.0ms	24×	body	256	valid
2.0ms	13×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify250.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

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: 32.5b

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)))
2.5b	(-.f64 x (tan.f64 x))
2.6b	(-.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))

series282.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
106.0ms	(-.f64 x (tan.f64 x))
53.0ms	(-.f64 x (sin.f64 x))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4877	1847
1	4877	1847

prune131.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Merged error: 0.0b

Counts

94 → 3

Compiler

Compiled 2523 to 853 computations (66.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 9/40)
20.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite29.0ms (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:

11.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
7.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)

series136.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

50.0ms	(*.f64 27/2800 (pow.f64 x 4))
50.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
36.0ms	(.f64 (.f64 x x) 9/40)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5488	873

prune84.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	69	3	72

Merged error: 0b

Counts

72 → 3

Compiler

Compiled 1344 to 968 computations (28% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 9/40)
20.3b	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))

rewrite29.0ms (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)))
7.0ms	(.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))
52.0ms	(-.f64 (-.f64 (.f64 (.f64 x x) 9/40) 1/2) (*.f64 27/2800 (pow.f64 x 4)))
35.0ms	(.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	5292	894

prune70.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	3	74

Merged error: 0b

Counts

74 → 3

Compiler

Compiled 1231 to 882 computations (28.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b	(-.f64 x (tan.f64 x))
2.5b	(-.f64 x (tan.f64 x))
2.5b	(-.f64 x (tan.f64 x))
2.6b	(-.f64 x (sin.f64 x))

rewrite24.0ms (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))

series322.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(-.f64 x (tan.f64 x))
92.0ms	(-.f64 x (tan.f64 x))
92.0ms	(-.f64 x (tan.f64 x))
41.0ms	(-.f64 x (sin.f64 x))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4784	858
1	4784	858

prune68.0ms (0.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	76	3	79

Merged error: 0b

Counts

79 → 3

Compiler

Compiled 2038 to 320 computations (84.3% saved)

regimes36.0ms (0.4%)

Compiler: Compiled 108 to 66 computations (38.9% saved)

bsearch51.0ms (0.5%)

Steps

Iters	Range		Point
10	0.001251924731406838	559472837561013.56	0.02695355388948877
9	-163621.55931441346	-0.002451113276326735	-0.027071839411171916

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	79	47
1	79	47

end0.0ms (0%)

sample6.2s (63.5%)

Algorithm

1×

intervals

Results

4.1s	1964×	body	2048	valid
1.2s	3015×	body	1024	valid
319.0ms	1561×	body	512	valid
144.0ms	114×	body	4096	valid
106.0ms	732×	body	256	valid
51.0ms	614×	body	128	valid

Compiler

Compiled 85 to 57 computations (32.9% saved)

Details

analyze1.4s (13.8%)

sample206.0ms (2.1%)

simplify250.0ms (2.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite29.0ms (0.3%)

series282.0ms (2.9%)

simplify74.0ms (0.8%)

prune131.0ms (1.3%)

localize9.0ms (0.1%)

rewrite29.0ms (0.3%)

series136.0ms (1.4%)

simplify58.0ms (0.6%)

prune84.0ms (0.9%)

localize9.0ms (0.1%)

rewrite29.0ms (0.3%)

series147.0ms (1.5%)

simplify57.0ms (0.6%)

prune70.0ms (0.7%)

localize12.0ms (0.1%)

rewrite24.0ms (0.2%)

series322.0ms (3.3%)

simplify99.0ms (1%)

prune68.0ms (0.7%)

regimes36.0ms (0.4%)

bsearch51.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.2s (63.5%)

Profiling