Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample94.0ms (1.6%)

Algorithm

1×

intervals

Results

45.0ms	111×	body	1024	valid
26.0ms	35×	body	2048	valid
10.0ms	45×	body	512	valid
3.0ms	52×	body	128	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify174.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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: 35.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.5b	(sin.f64 (+.f64 x eps))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182`
3×	`add-cube-cbrt_binary64_2178` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1_binary64_2204` `sin-sum_binary64_2276` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
1×	`diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `distribute-lft-out--_binary64_2095` `diff-sin_binary64_2293` `flip3--_binary64_2147` `associate--l+_binary64_2080` `difference-of-squares_binary64_2112`

Counts

2 → 26

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series102.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
34.0ms	(sin.f64 (+.f64 x eps))

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5018	441

prune63.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.3b

Counts

33 → 3

Compiler

Compiled 872 to 459 computations (47.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2143`
8×	`add-log-exp_binary64_2182`
7×	`add-sqr-sqrt_binary64_2165`
5×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `add-cbrt-cube_binary64_2179`
3×	`associate-r_binary64_2083` `sum-log_binary64_2234` `associate-l_binary64_2084` `distribute-lft-out_binary64_2094`
1×	`+-commutative_binary64_2073` `sin-cos-mult_binary64_2299` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-+r+_binary64_2075` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074`

Counts

3 → 41

Calls

3 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series158.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
33.0ms	(+.f64 x (+.f64 x eps))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4821	830
1	4821	830

prune127.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 0.2b

Counts

53 → 7

Compiler

Compiled 2147 to 1510 computations (29.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.4b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2174`
24×	`add-sqr-sqrt_binary64_2165`
15×	`associate-r_binary64_2083` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
10×	`unpow-prod-down_binary64_2222` `cube-prod_binary64_2171`
7×	`pow1_binary64_2204` `add-exp-log_binary64_2181`
6×	`add-cbrt-cube_binary64_2179`
5×	`unswap-sqr_binary64_2111`
4×	`add-log-exp_binary64_2182` `sqr-pow_binary64_2115`
3×	`pow-unpow_binary64_2220` `cube-mult_binary64_2173` `associate-l_binary64_2084` `unpow3_binary64_2209`
1×	`rem-cbrt-cube_binary64_2167` `pow-to-exp_binary64_2212` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `pow-pow_binary64_2215` `*-commutative_binary64_2074` `rem-cube-cbrt_binary64_2166` `pow-exp_binary64_2211` `pow1/3_binary64_2225`

Counts

4 → 85

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)

series250.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
82.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
34.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
31.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4871	1942
1	4871	1942

prune213.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Merged error: 0.2b

Counts

104 → 8

Compiler

Compiled 3689 to 2600 computations (29.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_2204` `add-sqr-sqrt_binary64_2165` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
1×	`cbrt-prod_binary64_2174` `cos-mult_binary64_2297` `cbrt-div_binary64_2175` `pow1/3_binary64_2225`

Counts

4 → 31

Calls

4 calls:

9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

series335.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
35.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
32.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4807	572
1	4807	572

prune117.0ms (2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	42	9	51

Merged error: 0.2b

Counts

51 → 9

Compiler

Compiled 2147 to 1454 computations (32.3% saved)

regimes96.0ms (1.7%)

Compiler: Compiled 438 to 354 computations (19.2% saved)

bsearch85.0ms (1.5%)

Steps

Iters	Range		Point
6	3.399893619986278e-45	2.058855698569637e-44	2.0358793251829584e-44
9	-1.144111223116443e-20	-1.4505402084482003e-27	-1.1289620862679035e-20

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms (0%)

sample3.4s (59.8%)

Algorithm

1×

intervals

Results

1.3s	3466×	body	1024	valid
924.0ms	1217×	body	2048	valid
511.0ms	1433×	body	512	valid
89.0ms	1270×	body	128	valid
86.0ms	614×	body	256	valid

Compiler

Compiled 276 to 222 computations (19.6% saved)

Details

analyze2.0ms (0%)

sample94.0ms (1.6%)

simplify174.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.3%)

series102.0ms (1.8%)

simplify59.0ms (1%)

prune63.0ms (1.1%)

localize12.0ms (0.2%)

rewrite25.0ms (0.4%)

series158.0ms (2.8%)

simplify85.0ms (1.5%)

prune127.0ms (2.2%)

localize17.0ms (0.3%)

rewrite32.0ms (0.6%)

series250.0ms (4.4%)

simplify93.0ms (1.6%)

prune213.0ms (3.7%)

localize18.0ms (0.3%)

rewrite32.0ms (0.6%)

series335.0ms (5.9%)

simplify80.0ms (1.4%)

prune117.0ms (2%)

regimes96.0ms (1.7%)

bsearch85.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (59.8%)

Profiling