Details

analyze16.8s (66%)

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)

sample99.0ms (0.4%)

Algorithm

1×

intervals

Results

52.0ms	153×	body	1024	valid
18.0ms	256×	pre	128	true
7.0ms	38×	body	512	valid
3.0ms	7×	body	2048	valid
2.0ms	21×	body	256	valid
2.0ms	37×	body	128	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	186	14
1	186	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: 13.8b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite23.0ms (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:

7.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
6.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
5.0ms	(tan.f64 (+.f64 y z))

series422.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

177.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
165.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
81.0ms	(tan.f64 (+.f64 y z))

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4838	932
1	4838	932

prune56.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	48	7	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Merged error: 0.1b

Counts

56 → 7

Compiler

Compiled 988 to 283 computations (71.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `cancel-sign-sub-inv_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
12.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
4.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series1.1s (4.3%)

Counts

4 → 12

Calls

4 calls:

602.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
285.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
102.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
97.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5225	2561

prune132.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.1b

Counts

107 → 10

Compiler

Compiled 2964 to 1035 computations (65.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`difference-of-squares_binary64`
9×	`associate-/r*_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out--_binary64`
5×	`associate-/l*_binary64` `tan-quot_binary64`
4×	`associate-/l/_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 110

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
12.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))))
6.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
6.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

series1.1s (4.3%)

Counts

4 → 12

Calls

4 calls:

628.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
290.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))))
117.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
64.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4971	3713
1	4971	3713

prune144.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Merged error: 0.1b

Counts

132 → 9

Compiler

Compiled 3994 to 1225 computations (69.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.4b	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
24.9b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`tan-quot_binary64`
11×	`*-un-lft-identity_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-prod_binary64`
6×	`add-log-exp_binary64` `cube-div_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

25.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)))) (tan.f64 a))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

series1.0s (4.1%)

Counts

4 → 12

Calls

4 calls:

622.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)))) (tan.f64 a))
193.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
111.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))
108.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4965	1780
1	4965	1780

prune104.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0.1b

Counts

105 → 9

Compiler

Compiled 2547 to 951 computations (62.7% saved)

regimes574.0ms (2.3%)

Compiler: Compiled 6658 to 4521 computations (32.1% 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%)

sample3.2s (12.6%)

Algorithm

1×

intervals

Results

1.2s	4600×	body	1024	valid
559.0ms	8000×	pre	128	true
233.0ms	1338×	body	512	valid
131.0ms	203×	body	2048	valid
73.0ms	1339×	body	128	valid
67.0ms	520×	body	256	valid

Compiler

Compiled 745 to 512 computations (31.3% saved)

Details

analyze16.8s (66%)

sample99.0ms (0.4%)

simplify109.0ms (0.4%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite23.0ms (0.1%)

series422.0ms (1.7%)

simplify107.0ms (0.4%)

prune56.0ms (0.2%)

localize15.0ms (0.1%)

rewrite43.0ms (0.2%)

series1.1s (4.3%)

simplify75.0ms (0.3%)

prune132.0ms (0.5%)

localize19.0ms (0.1%)

rewrite57.0ms (0.2%)

series1.1s (4.3%)

simplify72.0ms (0.3%)

prune144.0ms (0.6%)

localize17.0ms (0.1%)

rewrite47.0ms (0.2%)

series1.0s (4.1%)

simplify69.0ms (0.3%)

prune104.0ms (0.4%)

regimes574.0ms (2.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (12.6%)

Profiling