Details

analyze19.5s (38.8%)

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)

sample329.0ms (0.7%)

Algorithm

1×

intervals

Results

42.0ms	141×	body	1024	valid
19.0ms	256×	pre	128	true
9.0ms	51×	body	512	valid
3.0ms	22×	body	256	valid
3.0ms	6×	body	2048	valid
2.0ms	36×	body	128	valid

Compiler

Compiled 11574 to 10546 computations (8.9% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	186	14
1	186	14

prune5.0ms (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

13.4b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize18.0ms (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))
3.4b	(tan.f64 (+.f64 y z))

rewrite85.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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

Compiler

Compiled 790 to 187 computations (76.3% saved)

series1.9s (3.7%)

Error

12.5b

Counts

3 → 48

Calls

3 calls:

903.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
618.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
278.0ms	(tan.f64 (+.f64 y z))

Compiler

Compiled 2964 to 1700 computations (42.6% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5177	2610

prune136.0ms (0.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Error

0.1b

Counts

95 → 10

Compiler

Compiled 2227 to 703 computations (68.4% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
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 (/.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))

rewrite168.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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×	`associate-l_binary64` `associate-r_binary64` `sum-log_binary64` `distribute-lft-out_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_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` `frac-sub_binary64` `flip3--_binary64` `flip--_binary64` `times-frac_binary64` `associate-+r-_binary64` `frac-add_binary64`

Counts

4 → 71

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
14.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 1999 to 656 computations (67.2% saved)

series6.4s (12.7%)

Error

0.1b

Counts

4 → 57

Calls

4 calls:

3.3s	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
2.3s	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
336.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
329.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 5276 to 2711 computations (48.6% saved)

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4968	4670
1	4968	4670

prune221.0ms (0.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	127	11	138

Error

0.1b

Counts

138 → 11

Compiler

Compiled 4234 to 1420 computations (66.5% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite264.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

28×	`associate-*r/_binary64`
16×	`tan-quot_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`frac-sub_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `associate-/l/_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`
4×	`frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `associate--r+_binary64`
3×	`prod-exp_binary64` `cbrt-unprod_binary64` `times-frac_binary64` `associate-/l*_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-l/_binary64` `-commutative_binary64` `associate--l+_binary64`
1×	`frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64` `diff-log_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)))))
13.0ms	(-.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)))))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 4974 to 1477 computations (70.3% saved)

series5.0s (10%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

2.8s	(/.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)))))
1.5s	(-.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)))))
318.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
293.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

Compiler

Compiled 6748 to 3195 computations (52.7% saved)

simplify73.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5186	6802

prune309.0ms (0.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	144	12	156

Error

0.1b

Counts

156 → 12

Compiler

Compiled 7475 to 2270 computations (69.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 z) (sin.f64 y))
0.2b	(*.f64 (sin.f64 z) (sin.f64 y))
0.3b	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))
0.3b	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))

rewrite214.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`prod-exp_binary64` `cbrt-unprod_binary64`
8×	`pow1_binary64` `div-exp_binary64` `add-cube-cbrt_binary64` `cbrt-undiv_binary64` `*-un-lft-identity_binary64`
6×	`associate-l_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64` `sin-mult_binary64`
2×	`frac-2neg_binary64` `times-frac_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l/_binary64` `cos-mult_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))
8.0ms	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))
5.0ms	(*.f64 (sin.f64 z) (sin.f64 y))
5.0ms	(*.f64 (sin.f64 z) (sin.f64 y))

Compiler

Compiled 4584 to 1113 computations (75.7% saved)

series1.0s (2%)

Error

0.1b

Counts

4 → 28

Calls

4 calls:

338.0ms	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))
328.0ms	(/.f64 (.f64 (sin.f64 z) (sin.f64 y)) (.f64 (cos.f64 z) (cos.f64 y)))
146.0ms	(*.f64 (sin.f64 z) (sin.f64 y))
144.0ms	(*.f64 (sin.f64 z) (sin.f64 y))

Compiler

Compiled 3890 to 1861 computations (52.2% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4970	1678
1	4970	1678

prune212.0ms (0.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Error

0.1b

Counts

124 → 12

Compiler

Compiled 5618 to 1450 computations (74.2% saved)

regimes2.1s (4.2%)

Accuracy

Total 0.2b remaining (78.1%)

Threshold costs 0.2b (78.1%)

Compiler

Compiled 24934 to 16183 computations (35.1% saved)

bsearch0.0ms (0%)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	49
1	63	49

Remove

(sort y z)

Compiler

Compiled 60 to 44 computations (26.7% saved)

end0.0ms (0%)

sample12.0s (23.9%)

Algorithm

1×

intervals

Results

1.3s	4545×	body	1024	valid
562.0ms	8000×	pre	128	true
269.0ms	1387×	body	512	valid
146.0ms	216×	body	2048	valid
83.0ms	1307×	body	128	valid
71.0ms	545×	body	256	valid

Compiler

Compiled 362723 to 329774 computations (9.1% saved)

Details

analyze19.5s (38.8%)

sample329.0ms (0.7%)

simplify14.0ms (0%)

prune5.0ms (0%)

localize18.0ms (0%)

rewrite85.0ms (0.2%)

series1.9s (3.7%)

simplify48.0ms (0.1%)

prune136.0ms (0.3%)

localize15.0ms (0%)

rewrite168.0ms (0.3%)

series6.4s (12.7%)

simplify83.0ms (0.2%)

prune221.0ms (0.4%)

localize20.0ms (0%)

rewrite264.0ms (0.5%)

series5.0s (10%)

simplify73.0ms (0.1%)

prune309.0ms (0.6%)

localize26.0ms (0.1%)

rewrite214.0ms (0.4%)

series1.0s (2%)

simplify75.0ms (0.1%)

prune212.0ms (0.4%)

regimes2.1s (4.2%)

bsearch0.0ms (0%)

simplify12.0ms (0%)

end0.0ms (0%)

sample12.0s (23.9%)

Profiling