Details

analyze16.9s (60.5%)

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)

sample117.0ms (0.4%)

Algorithm

1×

intervals

Results

46.0ms	142×	body	1024	valid
18.0ms	256×	pre	128	true
12.0ms	9×	body	2048	valid
7.0ms	40×	body	512	valid
3.0ms	54×	body	128	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify176.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	177	14
1	177	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: 15.6b

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)))
0.1b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
3.4b	(tan.f64 (+.f64 y z))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`tan-quot_binary64`
3×	`pow1_binary64` `add-cube-cbrt_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` `associate-+r+_binary64`

Counts

3 → 40

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)))
6.0ms	(tan.f64 (+.f64 y z))

series767.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

333.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
302.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
132.0ms	(tan.f64 (+.f64 y z))

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	890
1	4939	890

prune53.0ms (0.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 0.1b

Counts

50 → 6

Compiler

Compiled 898 to 255 computations (71.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`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`
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 → 85

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
10.0ms	(/.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))

series2.0s (7.1%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
524.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
190.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
175.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4936	2543
1	4936	2543

prune142.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 0.0b

Counts

103 → 10

Compiler

Compiled 2918 to 1030 computations (64.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64`
101×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
23×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
17×	`distribute-lft-out_binary64`
16×	`associate-/r/_binary64` `tan-quot_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `frac-add_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `div-sub_binary64` `inv-pow_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 171

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z))))
9.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.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))

series1.5s (5.3%)

Counts

4 → 12

Calls

4 calls:

595.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z)))
533.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z))))
185.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
179.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5917	5721

prune236.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	183	10	193

Merged error: 0.0b

Counts

193 → 10

Compiler

Compiled 5839 to 2202 computations (62.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`associate-*l/_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-l_binary64`
9×	`associate-r_binary64`
8×	`associate-/l/_binary64`
6×	`frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `times-frac_binary64` `flip-+_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
8.0ms	(*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.0s (7.2%)

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
308.0ms	(*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a))
191.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
182.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	6769	2658

prune149.0ms (0.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

Compiler

Compiled 4424 to 1329 computations (70% saved)

regimes239.0ms (0.9%)

Compiler: Compiled 2523 to 1617 computations (35.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	32
1	53	32

end0.0ms (0%)

sample3.1s (11.1%)

Algorithm

1×

intervals

Results

1.4s	4532×	body	1024	valid
541.0ms	8000×	pre	128	true
252.0ms	1431×	body	512	valid
179.0ms	224×	body	2048	valid
70.0ms	1308×	body	128	valid
61.0ms	505×	body	256	valid

Compiler

Compiled 349 to 235 computations (32.7% saved)

Details

analyze16.9s (60.5%)

sample117.0ms (0.4%)

simplify176.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0%)

rewrite24.0ms (0.1%)

series767.0ms (2.7%)

simplify66.0ms (0.2%)

prune53.0ms (0.2%)

localize15.0ms (0.1%)

rewrite43.0ms (0.2%)

series2.0s (7.1%)

simplify75.0ms (0.3%)

prune142.0ms (0.5%)

localize16.0ms (0.1%)

rewrite53.0ms (0.2%)

series1.5s (5.3%)

simplify105.0ms (0.4%)

prune236.0ms (0.8%)

localize21.0ms (0.1%)

rewrite49.0ms (0.2%)

series2.0s (7.2%)

simplify71.0ms (0.3%)

prune149.0ms (0.5%)

regimes239.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (11.1%)

Profiling