Details

analyze707.0ms (9.1%)

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)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	65×	body	1024	valid
6.0ms	137×	body	128	valid
5.0ms	33×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify309.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5717	24

prune4.0ms (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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.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))

rewrite34.0ms (0.4%)

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:

7.0ms	(*.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)))

series639.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
99.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
92.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
86.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5715	1997

prune179.0ms (2.3%)

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 2660 to 1553 computations (41.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

317×	`*-un-lft-identity_binary64`
264×	`times-frac_binary64`
179×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
69×	`distribute-lft-out_binary64`
50×	`difference-of-squares_binary64`
36×	`associate-/r*_binary64`
25×	`distribute-lft-out--_binary64`
13×	`associate-/r/_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 251

Calls

4 calls:

20.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
13.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(+.f64 1 (tan.f64 x))

series759.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

410.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
220.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
76.0ms	(pow.f64 (tan.f64 x) 2)
52.0ms	(+.f64 1 (tan.f64 x))

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4968	9358
1	4968	9358

prune485.0ms (6.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	263	12	275

Merged error: 0.0b

Counts

275 → 12

Compiler

Compiled 7679 to 5074 computations (33.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/l*_binary64`
6×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`associate-/l/_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-plus_binary64` `div-sub_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64`

Counts

4 → 113

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(/.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))

series706.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

403.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
132.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
86.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
84.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	2925
1	4953	2925

prune148.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

Compiler

Compiled 3475 to 1377 computations (60.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`exp-prod_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64` `add-exp-log_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `distribute-lft-out_binary64` `unpow-prod-down_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 61

Calls

4 calls:

6.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
5.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
4.0ms	(+.f64 (tan.f64 x) 1)
3.0ms	(pow.f64 (tan.f64 x) 2)

series395.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
80.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
71.0ms	(pow.f64 (tan.f64 x) 2)
51.0ms	(+.f64 (tan.f64 x) 1)

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5000	701

prune81.0ms (1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	72	14	86

Merged error: 0.0b

Counts

86 → 14

Compiler

Compiled 1578 to 1055 computations (33.1% saved)

regimes472.0ms (6.1%)

Compiler: Compiled 5702 to 4184 computations (26.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample2.3s (29.7%)

Algorithm

1×

intervals

Results

426.0ms	1975×	body	1024	valid
198.0ms	4512×	body	128	valid
139.0ms	991×	body	512	valid
49.0ms	516×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 1443 to 1060 computations (26.5% saved)

Details

analyze707.0ms (9.1%)

sample37.0ms (0.5%)

simplify309.0ms (4%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite34.0ms (0.4%)

series639.0ms (8.2%)

simplify77.0ms (1%)

prune179.0ms (2.3%)

localize13.0ms (0.2%)

rewrite74.0ms (1%)

series759.0ms (9.7%)

simplify126.0ms (1.6%)

prune485.0ms (6.2%)

localize14.0ms (0.2%)

rewrite40.0ms (0.5%)

series706.0ms (9.1%)

simplify84.0ms (1.1%)

prune148.0ms (1.9%)

localize14.0ms (0.2%)

rewrite23.0ms (0.3%)

series395.0ms (5.1%)

simplify49.0ms (0.6%)

prune81.0ms (1%)

regimes472.0ms (6.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (29.7%)

Profiling