Details

analyze223.0ms (5.9%)

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)

sample50.0ms (1.3%)

Algorithm

1×

intervals

Results

26.0ms	64×	body	2048	valid
6.0ms	49×	body	512	valid
6.0ms	31×	body	1024	valid
3.0ms	88×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify23.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	364	12
1	364	12

prune6.0ms (0.2%)

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: 31.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.2b	(-.f64 1 (cos.f64 x))
15.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite16.0ms (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))

series78.0ms (2%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	700

prune62.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	9	51

Merged error: 0.0b

Counts

51 → 9

Compiler

Compiled 783 to 431 computations (45% saved)

localize12.0ms (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)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
15.7b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite39.0ms (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))

series263.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
88.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
30.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
15.0ms	(+.f64 1 (cos.f64 x))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	1781
1	4970	1781

prune108.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	125	7	132

Merged error: 0b

Counts

132 → 7

Compiler

Compiled 2164 to 1092 computations (49.5% saved)

localize9.0ms (0.2%)

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

rewrite32.0ms (0.8%)

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:

11.0ms	(*.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)

series264.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

124.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
105.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
35.0ms	(/.f64 (sin.f64 x) x)

simplify88.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5058	1953

prune101.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	114	7	121

Merged error: 0b

Counts

121 → 7

Compiler

Compiled 2066 to 1065 computations (48.5% saved)

localize9.0ms (0.2%)

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)))

rewrite28.0ms (0.7%)

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)

series333.0ms (8.8%)

Counts

3 → 9

Calls

3 calls:

160.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
139.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
34.0ms	(/.f64 (sin.f64 x) x)

simplify82.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4993	1539
1	4993	1539

prune74.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	96	7	103

Merged error: 0b

Counts

103 → 7

Compiler

Compiled 1573 to 774 computations (50.8% saved)

regimes32.0ms (0.8%)

Compiler: Compiled 210 to 156 computations (25.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample1.7s (45.9%)

Algorithm

1×

intervals

Results

843.0ms	2033×	body	2048	valid
225.0ms	1124×	body	1024	valid
189.0ms	1468×	body	512	valid
99.0ms	2485×	body	128	valid
66.0ms	787×	body	256	valid
42.0ms	103×	body	4096	valid

Compiler

Compiled 116 to 87 computations (25% saved)

Details

analyze223.0ms (5.9%)

sample50.0ms (1.3%)

simplify23.0ms (0.6%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite16.0ms (0.4%)

series78.0ms (2%)

simplify53.0ms (1.4%)

prune62.0ms (1.6%)

localize12.0ms (0.3%)

rewrite39.0ms (1%)

series263.0ms (6.9%)

simplify62.0ms (1.6%)

prune108.0ms (2.9%)

localize9.0ms (0.2%)

rewrite32.0ms (0.8%)

series264.0ms (6.9%)

simplify88.0ms (2.3%)

prune101.0ms (2.6%)

localize9.0ms (0.2%)

rewrite28.0ms (0.7%)

series333.0ms (8.8%)

simplify82.0ms (2.1%)

prune74.0ms (2%)

regimes32.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (45.9%)

Profiling