Details

analyze20.2s (57.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1110	98
1	1110	98
0	4	4
1	4	4

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

Symmetry

(sort y z)

Compiler

Compiled 45 to 37 computations (17.8% saved)

sample102.0ms (0.3%)

Algorithm

1×

intervals

Results

41.0ms	152×	body	1024	valid
18.0ms	256×	pre	128	true
7.0ms	39×	body	512	valid
3.0ms	6×	body	2048	valid
3.0ms	23×	body	256	valid
2.0ms	36×	body	128	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	186	14
1	186	14

prune13.0ms (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

Error

12.5b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize11.0ms (0%)

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))
3.8b	(tan.f64 (+.f64 y z))

rewrite73.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`tan-quot_binary64` `associate-+r+_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `diff-log_binary64` `frac-sub_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64` `sum-log_binary64` `distribute-lft-out_binary64`
1×	`flip3--_binary64` `flip--_binary64` `difference-of-squares_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-+r-_binary64` `+-commutative_binary64`

Counts

3 → 46

Calls

3 calls:

8.0ms	(-.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))

Compiler

Compiled 790 to 187 computations (76.3% saved)

series1.1s (3.1%)

Error

12.0b

Counts

3 → 42

Calls

3 calls:

545.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
364.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
138.0ms	(tan.f64 (+.f64 y z))

Compiler

Compiled 1995 to 1124 computations (43.7% saved)

simplify115.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4903	1742
1	4903	1742

prune82.0ms (0.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Error

0.0b

Counts

89 → 8

Compiler

Compiled 1550 to 377 computations (75.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite143.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-l_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l/_binary64` `associate-/r*_binary64`
2×	`flip3--_binary64` `flip--_binary64` `difference-of-squares_binary64` `frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-l/_binary64` `associate-r/_binary64` `*-commutative_binary64` `diff-log_binary64` `frac-sub_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64` `sum-log_binary64` `+-commutative_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_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))
9.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 2541 to 830 computations (67.3% saved)

series2.2s (6.2%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

1.3s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
446.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
204.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
168.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 3076 to 1659 computations (46.1% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5239	3527

prune151.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

0.0b

Counts

133 → 10

Compiler

Compiled 3736 to 1227 computations (67.2% saved)

localize17.0ms (0%)

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 (tan.f64 y) (tan.f64 z)) 3)))) (tan.f64 a))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.3b	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
25.3b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

rewrite150.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 84

Calls

4 calls:

26.0ms	(-.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))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
5.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

Compiler

Compiled 2495 to 1023 computations (59% saved)

series2.1s (6%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

1.3s	(-.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))
333.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
211.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))
188.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 3146 to 1840 computations (41.5% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5051	2657

prune138.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	118	10	128

Error

0.0b

Counts

128 → 10

Compiler

Compiled 3530 to 1300 computations (63.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite194.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`associate-*r/_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64` `tan-quot_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-r_binary64`
9×	`associate-l_binary64`
8×	`associate-/l/_binary64`
6×	`frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`times-frac_binary64` `frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/l_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `-commutative_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `distribute-lft-out_binary64`

Counts

4 → 98

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 (cos.f64 a) (+.f64 (tan.f64 y) (tan.f64 z))) (.f64 (sin.f64 a) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))))) (.f64 (cos.f64 a) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))))
8.0ms	(*.f64 (cos.f64 a) (+.f64 (tan.f64 y) (tan.f64 z)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 4540 to 1349 computations (70.3% saved)

series2.6s (7.5%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

1.7s	(/.f64 (-.f64 (.f64 (cos.f64 a) (+.f64 (tan.f64 y) (tan.f64 z))) (.f64 (sin.f64 a) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))))) (.f64 (cos.f64 a) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))))
422.0ms	(*.f64 (cos.f64 a) (+.f64 (tan.f64 y) (tan.f64 z)))
212.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
205.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 5637 to 2707 computations (52% saved)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4986	4704
1	4986	4704

prune193.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	138	9	147

Error

0.0b

Counts

147 → 9

Compiler

Compiled 6165 to 1771 computations (71.3% saved)

regimes1.2s (3.4%)

Accuracy

Total 0.2b remaining (74%)

Threshold costs 0.2b (74%)

Compiler

Compiled 14269 to 9644 computations (32.4% saved)

bsearch0.0ms (0%)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	35
1	55	35

Remove

(sort y z)

Compiler

Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

sample4.1s (11.6%)

Algorithm

1×

intervals

Results

1.2s	4613×	body	1024	valid
563.0ms	8000×	pre	128	true
252.0ms	1404×	body	512	valid
125.0ms	201×	body	2048	valid
75.0ms	1263×	body	128	valid
59.0ms	519×	body	256	valid

Compiler

Compiled 1553 to 1056 computations (32% saved)

Details

analyze20.2s (57.4%)

sample102.0ms (0.3%)

simplify15.0ms (0%)

prune13.0ms (0%)

localize11.0ms (0%)

rewrite73.0ms (0.2%)

series1.1s (3.1%)

simplify115.0ms (0.3%)

prune82.0ms (0.2%)

localize16.0ms (0%)

rewrite143.0ms (0.4%)

series2.2s (6.2%)

simplify89.0ms (0.3%)

prune151.0ms (0.4%)

localize17.0ms (0%)

rewrite150.0ms (0.4%)

series2.1s (6%)

simplify50.0ms (0.1%)

prune138.0ms (0.4%)

localize19.0ms (0.1%)

rewrite194.0ms (0.6%)

series2.6s (7.5%)

simplify93.0ms (0.3%)

prune193.0ms (0.5%)

regimes1.2s (3.4%)

bsearch0.0ms (0%)

simplify11.0ms (0%)

end0.0ms (0%)

sample4.1s (11.6%)

Profiling