Details

analyze1.6s (15.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14
0	1	1
1	1	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)

sample178.0ms (1.8%)

Algorithm

1×

intervals

Results

116.0ms	71×	body	2048	valid
33.0ms	82×	body	1024	valid
9.0ms	46×	body	512	valid
4.0ms	4×	body	4096	valid
3.0ms	21×	body	256	valid
3.0ms	32×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

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

Error

32.0b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.5b	(-.f64 x (tan.f64 x))
2.6b	(-.f64 x (sin.f64 x))

rewrite25.0ms (0.2%)

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))

series154.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

68.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
51.0ms	(-.f64 x (tan.f64 x))
34.0ms	(-.f64 x (sin.f64 x))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	6199	1847

prune83.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	6	94

Error

0.1b

Counts

94 → 6

Compiler

Compiled 1658 to 363 computations (78.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.3b	(*.f64 27/2800 (pow.f64 x 4))
13.6b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 60

Calls

3 calls:

8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(.f64 (.f64 x x) 9/40)
5.0ms	(*.f64 27/2800 (pow.f64 x 4))

series69.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
23.0ms	(*.f64 27/2800 (pow.f64 x 4))
18.0ms	(.f64 (.f64 x x) 9/40)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5451	873

prune70.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	69	6	75

Error

0.1b

Counts

75 → 6

Compiler

Compiled 1254 to 901 computations (28.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.0b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
2.5b	(-.f64 x (tan.f64 x))
2.5b	(-.f64 x (tan.f64 x))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
21×	`distribute-lft-out--_binary64`
15×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 118

Calls

4 calls:

33.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series283.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
61.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
46.0ms	(-.f64 x (tan.f64 x))
44.0ms	(-.f64 x (tan.f64 x))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4947	2684
1	4947	2684

prune95.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	130	6	136

Error

0.1b

Counts

136 → 6

Compiler

Compiled 2870 to 515 computations (82.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b	(-.f64 x (tan.f64 x))
2.5b	(-.f64 x (tan.f64 x))
2.5b	(-.f64 x (tan.f64 x))
2.6b	(-.f64 (/.f64 x (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))))

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
39×	`cancel-sign-sub-inv_binary64`
35×	`cbrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out--_binary64`
17×	`difference-of-squares_binary64`
12×	`add-log-exp_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-div_binary64` `associate-/r/_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-rgt-out--_binary64` `div-inv_binary64`
1×	`sub-div_binary64` `frac-sub_binary64`

Counts

4 → 114

Calls

4 calls:

53.0ms	(-.f64 (/.f64 x (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series468.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

337.0ms	(-.f64 (/.f64 x (cbrt.f64 (-.f64 x (tan.f64 x)))) (/.f64 (sin.f64 x) (cbrt.f64 (-.f64 x (tan.f64 x)))))
46.0ms	(-.f64 x (tan.f64 x))
43.0ms	(-.f64 x (tan.f64 x))
42.0ms	(-.f64 x (tan.f64 x))

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4937	3125
1	4937	3125

prune139.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	2	2
Picked	1	0	1
Done	1	2	3
Total	127	5	132

Error

0.1b

Counts

132 → 5

Compiler

Compiled 4870 to 932 computations (80.9% saved)

regimes113.0ms (1.1%)

Accuracy

Total 0.0b remaining (48.6%)

Threshold costs 0.0b (48.6%)

Compiler

Compiled 888 to 524 computations (41% saved)

bsearch46.0ms (0.5%)

Steps

Iters	Range		Point
8	0.0001374645270017353	0.05649206253518775	0.025060112129688804
8	-0.03657889531321138	-2.1145557048687787e-06	-0.02747742595770958

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	62
1	88	62

end0.0ms (0%)

sample6.1s (60.9%)

Algorithm

1×

intervals

Results

3.8s	1974×	body	2048	valid
1.1s	3070×	body	1024	valid
304.0ms	1505×	body	512	valid
108.0ms	97×	body	4096	valid
103.0ms	734×	body	256	valid
51.0ms	620×	body	128	valid

Compiler

Compiled 466 to 275 computations (41% saved)

Details

analyze1.6s (15.8%)

sample178.0ms (1.8%)

simplify77.0ms (0.8%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite25.0ms (0.2%)

series154.0ms (1.5%)

simplify81.0ms (0.8%)

prune83.0ms (0.8%)

localize9.0ms (0.1%)

rewrite26.0ms (0.3%)

series69.0ms (0.7%)

simplify61.0ms (0.6%)

prune70.0ms (0.7%)

localize8.0ms (0.1%)

rewrite57.0ms (0.6%)

series283.0ms (2.8%)

simplify72.0ms (0.7%)

prune95.0ms (1%)

localize14.0ms (0.1%)

rewrite79.0ms (0.8%)

series468.0ms (4.7%)

simplify95.0ms (0.9%)

prune139.0ms (1.4%)

regimes113.0ms (1.1%)

bsearch46.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.1s (60.9%)

Profiling