Details

analyze16.8s (56.1%)

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)

sample116.0ms (0.4%)

Algorithm

1×

intervals

Results

54.0ms	127×	body	1024	valid
18.0ms	256×	pre	128	true
14.0ms	10×	body	2048	valid
11.0ms	55×	body	512	valid
3.0ms	51×	body	128	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify178.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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: 11.5b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
4.0b	(tan.f64 (+.f64 y z))

rewrite26.0ms (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:

8.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
7.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
6.0ms	(tan.f64 (+.f64 y z))

series776.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

335.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
297.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
144.0ms	(tan.f64 (+.f64 y z))

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4826	932
1	4826	932

prune220.0ms (0.7%)

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 3698 to 2126 computations (42.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.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)))
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)))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

18.0ms	(/.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)))
11.0ms	(-.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)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.4s (8.1%)

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)))
708.0ms	(-.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)))
194.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
188.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify80.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6085	3599

prune589.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.1b

Counts

113 → 11

Compiler

Compiled 14042 to 6622 computations (52.8% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite78.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`
8×	`cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
6×	`distribute-lft-out_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-r_binary64` `tan-quot_binary64`
3×	`associate-/l/_binary64` `associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
2×	`associate-/r_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `div-inv_binary64` `flip--_binary64` `-commutative_binary64`
1×	`cos-mult_binary64` `unswap-sqr_binary64` `div-sub_binary64` `frac-times_binary64`

Counts

4 → 101

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (cos.f64 a) (sin.f64 z)) (cos.f64 z)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (.f64 (cos.f64 y) (cos.f64 z))) (/.f64 (.f64 (cos.f64 a) (sin.f64 y)) (cos.f64 y)))) (sin.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
11.0ms	(/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (*.f64 (cos.f64 y) (cos.f64 z)))
8.0ms	(.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series2.1s (7%)

Counts

4 → 12

Calls

4 calls:

1.4s	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (cos.f64 a) (sin.f64 z)) (cos.f64 z)) (+.f64 (/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (.f64 (cos.f64 y) (cos.f64 z))) (/.f64 (.f64 (cos.f64 a) (sin.f64 y)) (cos.f64 y)))) (sin.f64 a)) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
382.0ms	(/.f64 (.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z))) (*.f64 (cos.f64 y) (cos.f64 z)))
196.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
112.0ms	(.f64 (sin.f64 a) (.f64 (sin.f64 y) (sin.f64 z)))

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5566	4296

prune223.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 0.1b

Counts

124 → 11

Compiler

Compiled 7476 to 1698 computations (77.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
0.3b	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
27.6b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`associate-*l/_binary64`
16×	`tan-quot_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64`
8×	`associate-/l/_binary64` `cbrt-prod_binary64`
6×	`cube-div_binary64` `frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l_binary64` `times-frac_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `frac-add_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

21.0ms	(/.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 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))

series2.1s (6.9%)

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 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))) (cos.f64 a)))
345.0ms	(pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3)
205.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 y) (tan.f64 z)) 3))
181.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5091	2655

prune218.0ms (0.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	110	11	121

Merged error: 0.1b

Counts

121 → 11

Compiler

Compiled 5943 to 2297 computations (61.3% saved)

regimes349.0ms (1.2%)

Compiler: Compiled 4083 to 2422 computations (40.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	79
1	74	79

end0.0ms (0%)

sample3.2s (10.8%)

Algorithm

1×

intervals

Results

1.4s	4525×	body	1024	valid
540.0ms	8000×	pre	128	true
251.0ms	1370×	body	512	valid
222.0ms	248×	body	2048	valid
75.0ms	1345×	body	128	valid
64.0ms	512×	body	256	valid

Compiler

Compiled 479 to 289 computations (39.7% saved)

Details

analyze16.8s (56.1%)

sample116.0ms (0.4%)

simplify178.0ms (0.6%)

prune4.0ms (0%)

localize12.0ms (0%)

rewrite26.0ms (0.1%)

series776.0ms (2.6%)

simplify109.0ms (0.4%)

prune220.0ms (0.7%)

localize21.0ms (0.1%)

rewrite56.0ms (0.2%)

series2.4s (8.1%)

simplify80.0ms (0.3%)

prune589.0ms (2%)

localize35.0ms (0.1%)

rewrite78.0ms (0.3%)

series2.1s (7%)

simplify70.0ms (0.2%)

prune223.0ms (0.7%)

localize24.0ms (0.1%)

rewrite52.0ms (0.2%)

series2.1s (6.9%)

simplify58.0ms (0.2%)

prune218.0ms (0.7%)

regimes349.0ms (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (10.8%)

Profiling