Details

analyze17.3s (60.2%)

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)

sample110.0ms (0.4%)

Algorithm

1×

intervals

Results

40.0ms	127×	body	1024	valid
20.0ms	7×	body	2048	valid
19.0ms	256×	pre	128	true
11.0ms	56×	body	512	valid
3.0ms	46×	body	128	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify181.0ms (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: 12.1b

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 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
3.1b	(tan.f64 (+.f64 y z))

rewrite32.0ms (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:

13.0ms	(tan.f64 (+.f64 y z))
8.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
7.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))

series782.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

349.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
299.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
134.0ms	(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	4826	932
1	4826	932

prune176.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	47	8	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	8	56

Merged error: 0.1b

Counts

56 → 8

Compiler

Compiled 2911 to 1609 computations (44.7% saved)

localize17.0ms (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 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
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))

rewrite50.0ms (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:

17.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
15.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series2.5s (8.7%)

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))
1.0s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
197.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
173.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5111	2163

prune323.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 0.1b

Counts

91 → 11

Compiler

Compiled 6275 to 3336 computations (46.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
5×	`tan-quot_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `quot-tan_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

31.0ms	(-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 y) (cos.f64 y)) (/.f64 (sin.f64 z) (cos.f64 z))) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(/.f64 (sin.f64 z) (cos.f64 z))
5.0ms	(/.f64 (sin.f64 y) (cos.f64 y))

series1.4s (5%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 y) (cos.f64 y)) (/.f64 (sin.f64 z) (cos.f64 z))) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
198.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
47.0ms	(/.f64 (sin.f64 z) (cos.f64 z))
44.0ms	(/.f64 (sin.f64 y) (cos.f64 y))

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5034	2160

prune164.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	108	10	118

Merged error: 0.1b

Counts

118 → 10

Compiler

Compiled 4067 to 1416 computations (65.2% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64`
4×	`associate-/l*_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `tan-quot_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `quot-tan_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

37.0ms	(-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 y) (cos.f64 y)) (/.f64 (sin.f64 z) (cos.f64 z))) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
6.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
6.0ms	(*.f64 (tan.f64 y) (sin.f64 z))
5.0ms	(/.f64 (sin.f64 y) (cos.f64 y))

series1.6s (5.4%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 y) (cos.f64 y)) (/.f64 (sin.f64 z) (cos.f64 z))) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
218.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
132.0ms	(*.f64 (tan.f64 y) (sin.f64 z))
53.0ms	(/.f64 (sin.f64 y) (cos.f64 y))

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5273	2204

prune126.0ms (0.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	99	10	109

Merged error: 0.1b

Counts

109 → 10

Compiler

Compiled 3679 to 1035 computations (71.9% saved)

regimes296.0ms (1%)

Compiler: Compiled 3132 to 1878 computations (40% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	29
1	52	29

end0.0ms (0%)

sample3.2s (11.1%)

Algorithm

1×

intervals

Results

1.4s	4554×	body	1024	valid
558.0ms	8000×	pre	128	true
257.0ms	1372×	body	512	valid
214.0ms	215×	body	2048	valid
72.0ms	1340×	body	128	valid
64.0ms	519×	body	256	valid

Compiler

Compiled 359 to 226 computations (37% saved)

Details

analyze17.3s (60.2%)

sample110.0ms (0.4%)

simplify181.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0%)

rewrite32.0ms (0.1%)

series782.0ms (2.7%)

simplify107.0ms (0.4%)

prune176.0ms (0.6%)

localize17.0ms (0.1%)

rewrite50.0ms (0.2%)

series2.5s (8.7%)

simplify69.0ms (0.2%)

prune323.0ms (1.1%)

localize25.0ms (0.1%)

rewrite56.0ms (0.2%)

series1.4s (5%)

simplify70.0ms (0.2%)

prune164.0ms (0.6%)

localize23.0ms (0.1%)

rewrite63.0ms (0.2%)

series1.6s (5.4%)

simplify78.0ms (0.3%)

prune126.0ms (0.4%)

regimes296.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (11.1%)

Profiling