Details

analyze1.5s (15.2%)

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)

sample190.0ms (1.9%)

Algorithm

1×

intervals

Results

136.0ms	71×	body	2048	valid
30.0ms	96×	body	1024	valid
9.0ms	52×	body	512	valid
2.0ms	22×	body	128	valid
2.0ms	14×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify78.0ms (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

Merged error: 30.1b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.2b	(-.f64 x (tan.f64 x))
0.2b	(-.f64 x (sin.f64 x))

rewrite24.0ms (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))

series160.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

68.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
54.0ms	(-.f64 x (tan.f64 x))
38.0ms	(-.f64 x (sin.f64 x))

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6199	1847

prune78.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.0b

Counts

94 → 4

Compiler

Compiled 1645 to 357 computations (78.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
0.2b	(-.f64 x (tan.f64 x))
0.2b	(-.f64 x (sin.f64 x))

rewrite42.0ms (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:

14.0ms	(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))

series225.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
60.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
41.0ms	(-.f64 x (tan.f64 x))
20.0ms	(-.f64 x (sin.f64 x))

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4892	2756
1	4892	2756

prune106.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Merged error: 0.0b

Counts

144 → 4

Compiler

Compiled 2781 to 609 computations (78.1% 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)
16.8b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite23.0ms (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:

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

series65.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

24.0ms	(-.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)

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5451	873

prune71.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

Compiler

Compiled 1230 to 887 computations (27.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
0.2b	(-.f64 x (tan.f64 x))
0.4b	(pow.f64 (sin.f64 x) 3)
38.2b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

rewrite71.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
81×	`difference-of-squares_binary64`
75×	`times-frac_binary64`
66×	`unpow-prod-down_binary64` `cube-prod_binary64`
42×	`sqr-pow_binary64`
41×	`add-cube-cbrt_binary64`
26×	`distribute-lft-out--_binary64`
25×	`associate-/l*_binary64`
15×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`difference-cubes_binary64` `pow1_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 204

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))
12.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
3.0ms	(-.f64 x (tan.f64 x))
3.0ms	(pow.f64 (sin.f64 x) 3)

series272.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))
68.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
47.0ms	(-.f64 x (tan.f64 x))
25.0ms	(pow.f64 (sin.f64 x) 3)

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5070	7825

prune283.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	216	4	220

Merged error: 0.0b

Counts

220 → 4

Compiler

Compiled 8052 to 2442 computations (69.7% saved)

regimes97.0ms (1%)

Compiler: Compiled 734 to 426 computations (42% saved)

bsearch56.0ms (0.6%)

Steps

Iters	Range		Point
11	8.833665720540042e-29	0.06729445801273333	0.025924503586868625
9	-0.34099858593003163	-1.7266584988524147e-07	-0.027961819008046895

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	90	51
1	90	51

end0.0ms (0%)

sample6.1s (61.8%)

Algorithm

1×

intervals

Results

4.0s	1980×	body	2048	valid
1.0s	2971×	body	1024	valid
290.0ms	1534×	body	512	valid
125.0ms	124×	body	4096	valid
103.0ms	749×	body	256	valid
49.0ms	642×	body	128	valid

Compiler

Compiled 381 to 226 computations (40.7% saved)

Details

analyze1.5s (15.2%)

sample190.0ms (1.9%)

simplify78.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite24.0ms (0.2%)

series160.0ms (1.6%)

simplify82.0ms (0.8%)

prune78.0ms (0.8%)

localize10.0ms (0.1%)

rewrite42.0ms (0.4%)

series225.0ms (2.3%)

simplify126.0ms (1.3%)

prune106.0ms (1.1%)

localize9.0ms (0.1%)

rewrite23.0ms (0.2%)

series65.0ms (0.7%)

simplify64.0ms (0.6%)

prune71.0ms (0.7%)

localize15.0ms (0.2%)

rewrite71.0ms (0.7%)

series272.0ms (2.7%)

simplify122.0ms (1.2%)

prune283.0ms (2.8%)

regimes97.0ms (1%)

bsearch56.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.1s (61.8%)

Profiling