Details

analyze33.7s (58%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

Compiler

Compiled 45 to 37 computations (17.8% saved)

sample228.0ms (0.4%)

Algorithm

1×

intervals

Results

118.0ms	147×	body	1024	valid
38.0ms	256×	pre	128	true
19.0ms	45×	body	512	valid
17.0ms	6×	body	2048	valid
5.0ms	20×	body	256	valid
4.0ms	38×	body	128	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify305.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	177	14
1	177	14

prune8.0ms (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: 14.5b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize35.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
2.4b	(tan.f64 (+.f64 y z))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-+r+_binary64` `tan-quot_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 46

Calls

3 calls:

16.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
14.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
12.0ms	(tan.f64 (+.f64 y z))

series1.5s (2.6%)

Counts

3 → 9

Calls

3 calls:

654.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
567.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
268.0ms	(tan.f64 (+.f64 y z))

simplify227.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	4826	932
1	4826	932

prune135.0ms (0.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	46	9	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	9	56

Merged error: 0.1b

Counts

56 → 9

Compiler

Compiled 1041 to 310 computations (70.2% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.3b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite103.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
4×	`associate-+r+_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `times-frac_binary64` `flip--_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

34.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
31.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
13.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
10.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series4.9s (8.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
2.0s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
397.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
377.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify136.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5111	2163

prune218.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 0.1b

Counts

92 → 10

Compiler

Compiled 2540 to 923 computations (63.7% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
0.2b	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
0.3b	(*.f64 (tan.f64 z) (sin.f64 y))

rewrite133.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
4×	`times-frac_binary64` `associate-+r+_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-+r-_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

48.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
45.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
13.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
12.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

series4.8s (8.3%)

Counts

4 → 12

Calls

4 calls:

2.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a))
2.0s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)))) (tan.f64 a)))
388.0ms	(/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y))
251.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

simplify150.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4969	2514
1	4969	2514

prune228.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.1b

Counts

100 → 10

Compiler

Compiled 2972 to 998 computations (66.4% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)))) (tan.f64 a))
0.3b	(*.f64 (tan.f64 z) (sin.f64 y))
0.3b	(pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)
25.4b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3))

rewrite142.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
13×	`times-frac_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64` `unpow3_binary64` `tan-quot_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

86.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)))) (tan.f64 a))
13.0ms	(pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)
12.0ms	(*.f64 (tan.f64 z) (sin.f64 y))
8.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3))

series3.5s (6%)

Counts

4 → 12

Calls

4 calls:

2.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)))) (tan.f64 a))
677.0ms	(pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3)
409.0ms	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (tan.f64 z) (sin.f64 y)) (cos.f64 y)) 3))
267.0ms	(*.f64 (tan.f64 z) (sin.f64 y))

simplify102.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5187	2575

prune236.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	115	10	125

Merged error: 0.1b

Counts

125 → 10

Compiler

Compiled 3450 to 1168 computations (66.1% saved)

regimes1.4s (2.4%)

Compiler: Compiled 9748 to 6439 computations (33.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	34
1	62	34

end0.0ms (0%)

sample5.8s (9.9%)

Algorithm

1×

intervals

Results

2.2s	4506×	body	1024	valid
847.0ms	8000×	pre	128	true
428.0ms	1448×	body	512	valid
307.0ms	204×	body	2048	valid
113.0ms	1312×	body	128	valid
105.0ms	530×	body	256	valid

Compiler

Compiled 1043 to 695 computations (33.4% saved)

Details

analyze33.7s (58%)

sample228.0ms (0.4%)

simplify305.0ms (0.5%)

prune8.0ms (0%)

localize35.0ms (0.1%)

rewrite51.0ms (0.1%)

series1.5s (2.6%)

simplify227.0ms (0.4%)

prune135.0ms (0.2%)

localize42.0ms (0.1%)

rewrite103.0ms (0.2%)

series4.9s (8.4%)

simplify136.0ms (0.2%)

prune218.0ms (0.4%)

localize46.0ms (0.1%)

rewrite133.0ms (0.2%)

series4.8s (8.3%)

simplify150.0ms (0.3%)

prune228.0ms (0.4%)

localize49.0ms (0.1%)

rewrite142.0ms (0.2%)

series3.5s (6%)

simplify102.0ms (0.2%)

prune236.0ms (0.4%)

regimes1.4s (2.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.8s (9.9%)

Profiling