Details

analyze1.4s (15.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample192.0ms (2.1%)

Algorithm

1×

intervals

Results

127.0ms	74×	body	2048	valid
34.0ms	84×	body	1024	valid
9.0ms	43×	body	512	valid
8.0ms	30×	body	256	valid
2.0ms	2×	body	4096	valid
2.0ms	23×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify175.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	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: 34.7b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.0b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

3 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

series118.0ms (1.3%)

Counts

3 → 11

Calls

3 calls:

50.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
42.0ms	(-.f64 x (tan.f64 x))
26.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 231 to 189 computations (18.2% saved)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5612	1683

prune77.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Merged error: 0b

Counts

96 → 3

Compiler

Compiled 1508 to 296 computations (80.4% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
1×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

1 → 19

Calls

1 calls:

5.0ms

(*.f64 (*.f64 x x) 9/40)

series26.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

26.0ms

(*.f64 (*.f64 x x) 9/40)

Compiler

Compiled 42 to 42 computations (0% saved)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5175	182

prune19.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Merged error: 0b

Counts

25 → 3

Compiler

Compiled 241 to 165 computations (31.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.0b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
30×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 128

Calls

4 calls:

11.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series147.0ms (1.6%)

Counts

4 → 14

Calls

4 calls:

59.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
45.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
26.0ms	(-.f64 x (tan.f64 x))
16.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 319 to 275 computations (13.8% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5752	2440

prune97.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	142	3	145

Merged error: 0b

Counts

145 → 3

Compiler

Compiled 2538 to 509 computations (79.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
2.0b	(-.f64 x (tan.f64 x))
2.0b	(-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x)))
11.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (+.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
6×	`flip3--_binary64` `flip--_binary64`
4×	`cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `prod-exp_binary64` `sqr-sin-a_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow-prod-up_binary64` `associate--r-_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64` `-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (+.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))

series171.0ms (1.9%)

Counts

4 → 15

Calls

4 calls:

77.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x))) (*.f64 (+.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
38.0ms	(-.f64 x (tan.f64 x))
29.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
27.0ms	(-.f64 (.f64 x x) (.f64 (sin.f64 x) (sin.f64 x)))

Compiler

Compiled 491 to 350 computations (28.7% saved)

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5084	1591

prune78.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	106	3	109

Merged error: 0b

Counts

109 → 3

Compiler

Compiled 2338 to 448 computations (80.8% saved)

regimes85.0ms (0.9%)

Compiler: Compiled 442 to 282 computations (36.2% saved)

bsearch46.0ms (0.5%)

Steps

Iters	Range		Point
8	8.287038062754078e-05	3.932882794229564	0.004611415987775008
9	-8.993527003606488	-3.264713502883343e-05	-0.0055547518031396894

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	62
1	53	62

end0.0ms (0%)

sample6.1s (66.7%)

Algorithm

1×

intervals

Results

4.1s	2040×	body	2048	valid
1.0s	2963×	body	1024	valid
285.0ms	1493×	body	512	valid
112.0ms	104×	body	4096	valid
93.0ms	726×	body	256	valid
53.0ms	674×	body	128	valid

Compiler

Compiled 241 to 149 computations (38.2% saved)

Details

analyze1.4s (15.2%)

sample192.0ms (2.1%)

simplify175.0ms (1.9%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite24.0ms (0.3%)

series118.0ms (1.3%)

simplify71.0ms (0.8%)

prune77.0ms (0.8%)

localize4.0ms (0%)

rewrite7.0ms (0.1%)

series26.0ms (0.3%)

simplify73.0ms (0.8%)

prune19.0ms (0.2%)

localize9.0ms (0.1%)

rewrite38.0ms (0.4%)

series147.0ms (1.6%)

simplify78.0ms (0.9%)

prune97.0ms (1.1%)

localize11.0ms (0.1%)

rewrite32.0ms (0.3%)

series171.0ms (1.9%)

simplify43.0ms (0.5%)

prune78.0ms (0.9%)

regimes85.0ms (0.9%)

bsearch46.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (66.7%)

Profiling