Details

analyze16.7s (64%)

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)

sample100.0ms (0.4%)

Algorithm

1×

intervals

Results

33.0ms	135×	body	1024	valid
22.0ms	13×	body	2048	valid
18.0ms	256×	pre	128	true
8.0ms	44×	body	512	valid
2.0ms	47×	body	128	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 54 to 50 computations (7.4% saved)

simplify103.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	186	14
1	186	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: 10.4b

Counts

2 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize16.0ms (0.1%)

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))
1.6b	(tan.f64 (+.f64 y z))

rewrite23.0ms (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:

7.0ms	(-.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))

series406.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

175.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
154.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
77.0ms	(tan.f64 (+.f64 y z))

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4838	932
1	4838	932

prune61.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	48	7	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Merged error: 0.1b

Counts

56 → 7

Compiler

Compiled 1009 to 280 computations (72.2% saved)

localize13.0ms (0.1%)

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)))
0.2b	(-.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))

rewrite47.0ms (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:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
15.0ms	(+.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))
4.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

series1.4s (5.3%)

Counts

4 → 12

Calls

4 calls:

596.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
583.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
107.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
102.0ms	(+.f64 (tan.f64 y) (tan.f64 z))

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5115	2163

prune112.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 0.1b

Counts

90 → 8

Compiler

Compiled 2450 to 863 computations (64.8% saved)

localize23.0ms (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 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a)))
0.2b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a))
0.2b	(*.f64 (sin.f64 y) (sin.f64 z))
0.2b	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

21.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a)))
20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a))
8.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))
5.0ms	(*.f64 (sin.f64 y) (sin.f64 z))

series1.3s (5.1%)

Counts

4 → 12

Calls

4 calls:

597.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a))
595.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z))))) (tan.f64 a)))
107.0ms	(/.f64 (.f64 (sin.f64 y) (sin.f64 z)) (.f64 (cos.f64 y) (cos.f64 z)))
36.0ms	(*.f64 (sin.f64 y) (sin.f64 z))

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4998	2829
1	4998	2829

prune112.0ms (0.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 0.0b

Counts

99 → 7

Compiler

Compiled 3239 to 951 computations (70.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`tan-quot_binary64`
4×	`times-frac_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cos-mult_binary64` `associate-r/_binary64` `frac-add_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 83

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
10.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))
5.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
5.0ms	(*.f64 (sin.f64 y) (cos.f64 z))

series920.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

616.0ms	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (.f64 (cos.f64 y) (cos.f64 z))) (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
173.0ms	(/.f64 (+.f64 (.f64 (sin.f64 y) (cos.f64 z)) (.f64 (sin.f64 z) (cos.f64 y))) (*.f64 (cos.f64 y) (cos.f64 z)))
95.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
36.0ms	(*.f64 (sin.f64 y) (cos.f64 z))

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4944	2647
1	4944	2647

prune111.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Merged error: 0.0b

Counts

102 → 7

Compiler

Compiled 3633 to 831 computations (77.1% saved)

regimes815.0ms (3.1%)

Compiler: Compiled 10084 to 6595 computations (34.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	34
1	62	34

end0.0ms (0%)

sample3.3s (12.8%)

Algorithm

1×

intervals

Results

1.2s	4546×	body	1024	valid
542.0ms	8000×	pre	128	true
220.0ms	1386×	body	512	valid
134.0ms	229×	body	2048	valid
71.0ms	1317×	body	128	valid
59.0ms	522×	body	256	valid

Compiler

Compiled 1107 to 728 computations (34.2% saved)

Details

analyze16.7s (64%)

sample100.0ms (0.4%)

simplify103.0ms (0.4%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite23.0ms (0.1%)

series406.0ms (1.6%)

simplify105.0ms (0.4%)

prune61.0ms (0.2%)

localize13.0ms (0.1%)

rewrite47.0ms (0.2%)

series1.4s (5.3%)

simplify69.0ms (0.3%)

prune112.0ms (0.4%)

localize23.0ms (0.1%)

rewrite63.0ms (0.2%)

series1.3s (5.1%)

simplify74.0ms (0.3%)

prune112.0ms (0.4%)

localize24.0ms (0.1%)

rewrite50.0ms (0.2%)

series920.0ms (3.5%)

simplify76.0ms (0.3%)

prune111.0ms (0.4%)

regimes815.0ms (3.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (12.8%)

Profiling