Details

analyze1.0s (10.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample92.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	33×	body	2048	valid
13.0ms	46×	body	1024	valid
11.0ms	141×	body	128	valid
11.0ms	3×	body	4096	valid
4.0ms	26×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	1×	body	8192	exit
0.0ms	7×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify392.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	299	20
1	299	20

prune8.0ms (0.1%)

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

16.2b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

3.3b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.0b	(-.f64 (.f64 PI.f64 l) (/.f64 (tan.f64 (.f64 PI.f64 l)) (*.f64 F F)))
0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
3.3b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
27.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 66

Calls

8 calls:

11.0ms	(*.f64 PI.f64 l)
7.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
3.0ms	(*.f64 PI.f64 l)
3.0ms	(tan.f64 (*.f64 PI.f64 l))
0.0ms	(-.f64 (.f64 PI.f64 l) (/.f64 (tan.f64 (.f64 PI.f64 l)) (*.f64 F F)))

series377.0ms (3.7%)

Counts

4 → 15

Calls

4 calls:

245.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
89.0ms	(tan.f64 (*.f64 PI.f64 l))
24.0ms	(*.f64 PI.f64 l)
18.0ms	(*.f64 PI.f64 l)

Compiler

Compiled 450 to 295 computations (34.4% saved)

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5862	910

prune180.0ms (1.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	64	17	81
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	18	83

Error

12.9b

Counts

83 → 18

Compiler

Compiled 1608 to 426 computations (73.5% saved)

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
0.1b	(/.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) F) F)
0.0b	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 PI.f64 l)) F) F))
0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.2b	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
27.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 72

Calls

8 calls:

4.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))
0.0ms	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 PI.f64 l)) F) F))

series309.0ms (3%)

Counts

4 → 15

Calls

4 calls:

231.0ms	(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
40.0ms	(tan.f64 (*.f64 PI.f64 l))
20.0ms	(*.f64 PI.f64 l)
18.0ms	(*.f64 PI.f64 l)

Compiler

Compiled 448 to 281 computations (37.3% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4823	1012
1	4823	1012

prune127.0ms (1.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	86	19	105

Error

12.9b

Counts

105 → 19

Compiler

Compiled 1777 to 507 computations (71.5% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))) F)
0.2b	(*.f64 PI.f64 l)
0.1b	(/.f64 (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))) F) F)
0.0b	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))) F) F))
0.3b	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
27.6b	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-r_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

8 calls:

10.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
3.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))) F) F))

series99.0ms (1%)

Counts

4 → 6

Calls

4 calls:

63.0ms	(tan.f64 (.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64))))
36.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 l (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 172 to 110 computations (36% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5073	469

prune89.0ms (0.9%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	2	15	17
Picked	0	1	1
Done	0	1	1
Total	61	19	80

Error

12.9b

Counts

80 → 19

Compiler

Compiled 1389 to 545 computations (60.8% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(/.f64 (tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (*.f64 l (sqrt.f64 PI.f64)))) F)
0.1b	(/.f64 (/.f64 (tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (*.f64 l (sqrt.f64 PI.f64)))) F) F)
0.0b	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (.f64 l (sqrt.f64 PI.f64)))) F) F))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
27.8b	(tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (*.f64 l (sqrt.f64 PI.f64))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`tan-quot_binary64`

Counts

4 → 47

Calls

8 calls:

3.0ms	(tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (*.f64 l (sqrt.f64 PI.f64))))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(-.f64 (.f64 PI.f64 l) (/.f64 (/.f64 (tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (.f64 l (sqrt.f64 PI.f64)))) F) F))

series47.0ms (0.5%)

Counts

4 → 3

Calls

4 calls:

47.0ms	(tan.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))) (*.f64 l (sqrt.f64 PI.f64))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 100 to 62 computations (38% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4994	369
1	4994	369

prune70.0ms (0.7%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	2	14	16
Picked	0	1	1
Done	1	1	2
Total	50	19	69

Error

12.9b

Counts

69 → 19

Compiler

Compiled 1134 to 342 computations (69.8% saved)

simplify34.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	1036	1633
1	1036	1633

regimes621.0ms (6%)

Accuracy

Total 0.7b remaining (5.9%)

Threshold costs 0.7b (5.9%)

Compiler

Compiled 5284 to 3150 computations (40.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms (0%)

sample6.3s (61.5%)

Algorithm

1×

intervals

Results

1.1s	1060×	body	2048	valid
561.0ms	1837×	body	1024	valid
258.0ms	4039×	body	128	valid
225.0ms	59×	body	4096	valid
147.0ms	698×	body	512	valid
43.0ms	307×	body	256	valid
13.0ms	189×	body	128	invalid
3.0ms	8×	body	2048	invalid
1.0ms	2×	body	8192	exit

Compiler

Compiled 2850 to 1681 computations (41% saved)

Pareto

0.7317652703371541

Details

analyze1.0s (10.2%)

sample92.0ms (0.9%)

simplify392.0ms (3.8%)

prune8.0ms (0.1%)

localize10.0ms (0.1%)

rewrite30.0ms (0.3%)

series377.0ms (3.7%)

simplify86.0ms (0.8%)

prune180.0ms (1.7%)

localize8.0ms (0.1%)

rewrite19.0ms (0.2%)

series309.0ms (3%)

simplify92.0ms (0.9%)

prune127.0ms (1.2%)

localize13.0ms (0.1%)

rewrite24.0ms (0.2%)

series99.0ms (1%)

simplify89.0ms (0.9%)

prune89.0ms (0.9%)

localize25.0ms (0.2%)

rewrite11.0ms (0.1%)

series47.0ms (0.5%)

simplify65.0ms (0.6%)

prune70.0ms (0.7%)

simplify34.0ms (0.3%)

regimes621.0ms (6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.3s (61.5%)

Profiling