Details

analyze243.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample60.0ms (1.8%)

Algorithm

1×

intervals

Results

29.0ms	55×	body	2560	valid
10.0ms	40×	body	1280	valid
7.0ms	41×	body	640	valid
3.0ms	28×	body	320	valid
3.0ms	79×	body	80	valid
1.0ms	13×	body	160	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	367	12
1	367	12

prune3.0ms (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: 31.0b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.7b	(-.f64 1 (cos.f64 x))
16.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series9.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1 (cos.f64 x))

simplify73.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4911	700
1	4911	700

prune56.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Merged error: 0.0b

Counts

51 → 6

Compiler

Compiled 734 to 406 computations (44.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
16.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`pow1_binary64` `associate-/l*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `div-sub_binary64` `sqr-sin-a_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series33.0ms (1%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
13.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

simplify100.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4991	1781
1	4991	1781

prune85.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	124	5	129

Merged error: 0b

Counts

129 → 5

Compiler

Compiled 2145 to 1077 computations (49.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 (sin.f64 x) x)

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
6×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64`
5×	`pow1_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `tan-quot_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 105

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series34.0ms (1%)

Counts

3 → 9

Calls

3 calls:

17.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
13.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

simplify97.0ms (3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4957	1953
1	4957	1953

prune75.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Merged error: 0b

Counts

119 → 5

Compiler

Compiled 2047 to 1051 computations (48.7% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
6×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `tan-quot_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `associate-r_binary64` `div-inv_binary64`
2×	`associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

3 → 87

Calls

3 calls:

9.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series34.0ms (1%)

Counts

3 → 9

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
14.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
4.0ms	(/.f64 (sin.f64 x) x)

simplify110.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4946	1539
1	4946	1539

prune51.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Merged error: 0b

Counts

101 → 5

Compiler

Compiled 1573 to 772 computations (50.9% saved)

regimes22.0ms (0.7%)

Compiler: Compiled 71 to 52 computations (26.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample2.0s (61.4%)

Algorithm

1×

intervals

Results

797.0ms	1557×	body	2560	valid
329.0ms	1273×	body	1280	valid
252.0ms	1522×	body	640	valid
108.0ms	906×	body	320	valid
79.0ms	2268×	body	80	valid
43.0ms	474×	body	160	valid

Compiler

Compiled 89 to 66 computations (25.8% saved)

Details

analyze243.0ms (7.5%)

sample60.0ms (1.8%)

simplify29.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.4%)

series9.0ms (0.3%)

simplify73.0ms (2.3%)

prune56.0ms (1.7%)

localize10.0ms (0.3%)

rewrite33.0ms (1%)

series33.0ms (1%)

simplify100.0ms (3.1%)

prune85.0ms (2.6%)

localize9.0ms (0.3%)

rewrite23.0ms (0.7%)

series34.0ms (1%)

simplify97.0ms (3%)

prune75.0ms (2.3%)

localize9.0ms (0.3%)

rewrite24.0ms (0.8%)

series34.0ms (1%)

simplify110.0ms (3.4%)

prune51.0ms (1.6%)

regimes22.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (61.4%)

Profiling