Details

analyze704.0ms (11.7%)

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)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	57×	body	1024	valid
7.0ms	161×	body	128	valid
4.0ms	26×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify292.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.6%)

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` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series646.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
92.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
92.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
92.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune635.0ms (10.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 0.0b

Counts

123 → 10

Compiler

Compiled 10147 to 7002 computations (31% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`pow1_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64` `cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
5×	`frac-times_binary64`
4×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64` `tan-quot_binary64`
3×	`sub-neg_binary64` `swap-sqr_binary64` `associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 95

Calls

4 calls:

12.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(+.f64 (tan.f64 x) 1)
4.0ms	(-.f64 1 (tan.f64 x))

series332.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
83.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
53.0ms	(-.f64 1 (tan.f64 x))
49.0ms	(+.f64 (tan.f64 x) 1)

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5219	1370

prune170.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

Compiler

Compiled 3355 to 1993 computations (40.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
0.2b	(+.f64 (tan.f64 x) 1)
0.2b	(exp.f64 (+.f64 (tan.f64 x) 1))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
8×	`exp-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`log-prod_binary64` `tan-quot_binary64`
3×	`swap-sqr_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
5.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
5.0ms	(+.f64 (tan.f64 x) 1)

series395.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
88.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
75.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
41.0ms	(+.f64 (tan.f64 x) 1)

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5033	736

prune119.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	83	11	94

Merged error: 0.0b

Counts

94 → 11

Compiler

Compiled 2343 to 1430 computations (39% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.4b	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
24×	`exp-prod_binary64`
18×	`exp-sum_binary64`
17×	`add-cube-cbrt_binary64`
16×	`cancel-sign-sub-inv_binary64` `difference-of-squares_binary64`
13×	`pow1_binary64` `log-pow_binary64` `unpow-prod-down_binary64`
12×	`log-prod_binary64`
7×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`tan-quot_binary64`
3×	`pow-unpow_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`sub-neg_binary64` `rem-exp-log_binary64` `exp-diff_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `pow-pow_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `log-div_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

10.0ms	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
9.0ms	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series644.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
149.0ms	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))
83.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
74.0ms	(pow.f64 (tan.f64 x) 2)

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4979	1187
1	4979	1187

prune211.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	125	9	134

Merged error: 0.0b

Counts

134 → 9

Compiler

Compiled 3654 to 2355 computations (35.6% saved)

regimes50.0ms (0.8%)

Compiler: Compiled 430 to 316 computations (26.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	31
1	25	31

end0.0ms (0%)

sample1.2s (20.1%)

Algorithm

1×

intervals

Results

422.0ms	1973×	body	1024	valid
194.0ms	4532×	body	128	valid
138.0ms	958×	body	512	valid
51.0ms	525×	body	256	valid
4.0ms	12×	body	2048	valid

Compiler

Compiled 247 to 178 computations (27.9% saved)

Details

analyze704.0ms (11.7%)

sample34.0ms (0.6%)

simplify292.0ms (4.9%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series646.0ms (10.8%)

simplify103.0ms (1.7%)

prune635.0ms (10.6%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series332.0ms (5.5%)

simplify75.0ms (1.2%)

prune170.0ms (2.8%)

localize13.0ms (0.2%)

rewrite27.0ms (0.5%)

series395.0ms (6.6%)

simplify84.0ms (1.4%)

prune119.0ms (2%)

localize13.0ms (0.2%)

rewrite42.0ms (0.7%)

series644.0ms (10.7%)

simplify101.0ms (1.7%)

prune211.0ms (3.5%)

regimes50.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (20.1%)

Profiling