Details

analyze515.0ms (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	57×	body	1280	valid
10.0ms	53×	body	640	valid
5.0ms	123×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify662.0ms (14.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	5728	24

prune5.0ms (0.1%)

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: 0.4b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series79.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
21.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
11.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4969	1997
1	4969	1997

prune144.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 0.1b

Counts

122 → 12

Compiler

Compiled 2683 to 1572 computations (41.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.2b	(/.f64 1 (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
329×	`*-un-lft-identity_binary64`
267×	`add-sqr-sqrt_binary64`
136×	`difference-of-squares_binary64`
131×	`add-cube-cbrt_binary64`
54×	`associate-/r*_binary64`
48×	`distribute-lft-out_binary64`
40×	`unpow-prod-down_binary64`
36×	`unpow2_binary64` `sqr-pow_binary64`
17×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64`
5×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `pow-pow_binary64` `rec-exp_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 296

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
6.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series67.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (pow.f64 (tan.f64 x) 2))))
10.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
10.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)

simplify143.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5036	9003

prune406.0ms (9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	309	11	320

Merged error: 0.1b

Counts

320 → 11

Compiler

Compiled 7823 to 5643 computations (27.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
55×	`log-pow_binary64`
54×	`exp-prod_binary64`
48×	`times-frac_binary64`
40×	`difference-of-squares_binary64`
26×	`add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64` `unpow2_binary64` `sqr-pow_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `add-exp-log_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-cbrt-cube_binary64`
3×	`log-prod_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `associate-/r/_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `div-sub_binary64` `div-inv_binary64` `log-div_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 123

Calls

4 calls:

21.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))
6.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series66.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))
10.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5038	2076

prune143.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	134	12	146

Merged error: 0.1b

Counts

146 → 12

Compiler

Compiled 3250 to 2336 computations (28.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64` `tan-quot_binary64`
3×	`associate-/r_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_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×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
6.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series54.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
16.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
10.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify92.0ms (2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5002	1297

prune56.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	95	12	107

Merged error: 0.1b

Counts

107 → 12

Compiler

Compiled 2113 to 780 computations (63.1% saved)

regimes77.0ms (1.7%)

Compiler: Compiled 572 to 454 computations (20.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	24
1	23	24

end0.0ms (0%)

sample1.5s (34.2%)

Algorithm

1×

intervals

Results

381.0ms	1481×	body	1280	valid
219.0ms	1288×	body	640	valid
165.0ms	4315×	body	80	valid
73.0ms	597×	body	320	valid
27.0ms	319×	body	160	valid

Compiler

Compiled 314 to 247 computations (21.3% saved)

Details

analyze515.0ms (11.4%)

sample41.0ms (0.9%)

simplify662.0ms (14.6%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite46.0ms (1%)

series79.0ms (1.7%)

simplify96.0ms (2.1%)

prune144.0ms (3.2%)

localize10.0ms (0.2%)

rewrite54.0ms (1.2%)

series67.0ms (1.5%)

simplify143.0ms (3.2%)

prune406.0ms (9%)

localize12.0ms (0.3%)

rewrite39.0ms (0.9%)

series66.0ms (1.5%)

simplify119.0ms (2.6%)

prune143.0ms (3.2%)

localize14.0ms (0.3%)

rewrite25.0ms (0.6%)

series54.0ms (1.2%)

simplify92.0ms (2%)

prune56.0ms (1.2%)

regimes77.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (34.2%)

Profiling