Details

analyze1.4s (9.3%)

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)

sample170.0ms (1.1%)

Algorithm

1×

intervals

Results

95.0ms	56×	body	2048	valid
42.0ms	110×	body	1024	valid
9.0ms	7×	body	4096	valid
7.0ms	31×	body	512	valid
5.0ms	33×	body	256	valid
2.0ms	19×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify252.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	990	14
1	990	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: 33.8b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.3b	(-.f64 x (sin.f64 x))
1.5b	(-.f64 x (tan.f64 x))

rewrite30.0ms (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:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
5.0ms	(-.f64 x (sin.f64 x))

series306.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

134.0ms	(-.f64 x (tan.f64 x))
121.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
51.0ms	(-.f64 x (sin.f64 x))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4877	1847
1	4877	1847

prune93.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 0.1b

Counts

94 → 5

Compiler

Compiled 1654 to 360 computations (78.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
17.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite29.0ms (0.2%)

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:

9.0ms	(-.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)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))

series152.0ms (1%)

Counts

3 → 9

Calls

3 calls:

57.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
51.0ms	(*.f64 27/2800 (pow.f64 x 4))
44.0ms	(.f64 (.f64 x x) 9/40)

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5488	873

prune75.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Merged error: 0.1b

Counts

74 → 6

Compiler

Compiled 1280 to 924 computations (27.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))) 6)
13.6b	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
21.1b	(-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6))
25.3b	(/.f64 (-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6)) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`unpow-prod-down_binary64`
10×	`cancel-sign-sub-inv_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-/l_binary64`
2×	`cbrt-div_binary64` `flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 87

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6)) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))
10.0ms	(-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6))
5.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))) 6)
3.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series1.5s (10.1%)

Counts

4 → 12

Calls

4 calls:

805.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))) 6)
407.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
158.0ms	(-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6))
124.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6)) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5648	3229

prune247.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	98	7	105

Merged error: 0.1b

Counts

105 → 7

Compiler

Compiled 4017 to 3255 computations (19% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.6b	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
13.6b	(cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800)))
26.9b	(-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3))
27.9b	(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3)) (.f64 (+.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) (.f64 (.f64 x x) 9/40)) (+.f64 (.f64 (pow.f64 x 8) 6561/2560000) (+.f64 (pow.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) 4) (.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800))) 6))))))

rewrite131.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`add-sqr-sqrt_binary64`
70×	`unpow-prod-down_binary64`
60×	`difference-of-squares_binary64`
51×	`sqr-pow_binary64`
34×	`cube-prod_binary64`
26×	`cancel-sign-sub-inv_binary64`
25×	`associate-/l*_binary64` `times-frac_binary64`
24×	`cbrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `frac-times_binary64`
3×	`difference-cubes_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow1/3_binary64` `div-exp_binary64` `flip--_binary64` `associate-l/_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` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 161

Calls

4 calls:

52.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3)) (.f64 (+.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) (.f64 (.f64 x x) 9/40)) (+.f64 (.f64 (pow.f64 x 8) 6561/2560000) (+.f64 (pow.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) 4) (.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800))) 6))))))
25.0ms	(-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3))
3.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800)))
3.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series1.2s (8%)

Counts

4 → 12

Calls

4 calls:

411.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
403.0ms	(cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800)))
207.0ms	(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3)) (.f64 (+.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) (.f64 (.f64 x x) 9/40)) (+.f64 (.f64 (pow.f64 x 8) 6561/2560000) (+.f64 (pow.f64 (+.f64 1/2 (.f64 (pow.f64 x 4) 27/2800)) 4) (.f64 (.f64 (pow.f64 x 4) 81/1600) (pow.f64 (cbrt.f64 (+.f64 1/2 (*.f64 (pow.f64 x 4) 27/2800))) 6))))))
171.0ms	(-.f64 (pow.f64 (.f64 (pow.f64 x 4) 81/1600) 3) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))) 6) 3))

simplify157.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5085	11428

prune1.3s (8.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	173	7	180

Merged error: 0.1b

Counts

180 → 7

Compiler

Compiled 14214 to 12160 computations (14.5% saved)

regimes252.0ms (1.7%)

Compiler: Compiled 2644 to 2018 computations (23.7% saved)

bsearch50.0ms (0.3%)

Steps

Iters	Range		Point
7	0.01830935325231879	1.3650797940298596	0.0363653530648353
9	-24107.01994091685	-0.020673903178957394	-1.5604285908945796

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	99	87
1	99	87

end0.0ms (0%)

sample7.2s (48.5%)

Algorithm

1×

intervals

Results

4.0s	2008×	body	2048	valid
1.2s	3074×	body	1024	valid
305.0ms	1432×	body	512	valid
165.0ms	128×	body	4096	valid
103.0ms	754×	body	256	valid
50.0ms	604×	body	128	valid

Compiler

Compiled 1332 to 1015 computations (23.8% saved)

Details

analyze1.4s (9.3%)

sample170.0ms (1.1%)

simplify252.0ms (1.7%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite30.0ms (0.2%)

series306.0ms (2.1%)

simplify79.0ms (0.5%)

prune93.0ms (0.6%)

localize9.0ms (0.1%)

rewrite29.0ms (0.2%)

series152.0ms (1%)

simplify61.0ms (0.4%)

prune75.0ms (0.5%)

localize18.0ms (0.1%)

rewrite51.0ms (0.3%)

series1.5s (10.1%)

simplify68.0ms (0.5%)

prune247.0ms (1.7%)

localize37.0ms (0.2%)

rewrite131.0ms (0.9%)

series1.2s (8%)

simplify157.0ms (1.1%)

prune1.3s (8.8%)

regimes252.0ms (1.7%)

bsearch50.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.2s (48.5%)

Profiling