Details

analyze104.0ms (2.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

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)

sample69.0ms (1.4%)

Algorithm

1×

intervals

Results

30.0ms	110×	body	1024	valid
19.0ms	40×	body	2048	valid
8.0ms	42×	body	512	valid
3.0ms	24×	body	256	valid
2.0ms	40×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.2%)

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: 36.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.7b	(sin.f64 (+.f64 x eps))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
2×	`pow1_binary64_2185` `sin-sum_binary64_2257` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-sin_binary64_2274` `diff-log_binary64_2216` `associate--l+_binary64_2061` `sub-neg_binary64_2117`

Counts

2 → 26

Calls

2 calls:

12.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series51.0ms (1%)

Counts

2 → 6

Calls

2 calls:

33.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
18.0ms	(sin.f64 (+.f64 x eps))

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5196	441

prune27.0ms (0.5%)

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 428 to 129 computations (69.9% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163`
7×	`add-sqr-sqrt_binary64_2146`
5×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `associate-l_binary64_2065` `associate-r_binary64_2064`
1×	`pow-prod-down_binary64_2195` `sin-cos-mult_binary64_2280` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `associate-+r+_binary64_2056` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`

Counts

3 → 41

Calls

3 calls:

7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
5.0ms	(+.f64 x (+.f64 x eps))

series83.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(+.f64 x (+.f64 x eps))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5266	830

prune67.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 0.3b

Counts

53 → 9

Compiler

Compiled 1183 to 773 computations (34.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(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)
3.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2155`
24×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `*-un-lft-identity_binary64_2124`
10×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
7×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
6×	`add-cbrt-cube_binary64_2160`
5×	`unswap-sqr_binary64_2092`
4×	`add-log-exp_binary64_2163` `sqr-pow_binary64_2096`
3×	`unpow3_binary64_2190` `pow-unpow_binary64_2201` `cube-mult_binary64_2154` `associate-l_binary64_2065`
1×	`pow-prod-down_binary64_2195` `pow-pow_binary64_2196` `rem-cbrt-cube_binary64_2148` `pow-exp_binary64_2192` `*-commutative_binary64_2055` `pow1/3_binary64_2206` `prod-exp_binary64_2173` `pow-to-exp_binary64_2193` `cbrt-unprod_binary64_2157` `rem-cube-cbrt_binary64_2147`

Counts

4 → 85

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series141.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
47.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
20.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4910	1942
1	4910	1942

prune131.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	96	10	106

Merged error: 0.3b

Counts

106 → 10

Compiler

Compiled 2485 to 1655 computations (33.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
1.1b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
3.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_2155`
11×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`unpow-prod-down_binary64_2203`
5×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
4×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `sqr-pow_binary64_2096`
2×	`pow1/3_binary64_2206`
1×	`pow-pow_binary64_2196` `pow-exp_binary64_2192` `pow-to-exp_binary64_2193`

Counts

4 → 57

Calls

4 calls:

7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
2.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))

series236.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
59.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
20.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4885	1513
1	4885	1513

prune93.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	71	8	79

Merged error: 0.3b

Counts

79 → 8

Compiler

Compiled 1731 to 1209 computations (30.2% saved)

regimes265.0ms (5.4%)

Compiler: Compiled 1734 to 1417 computations (18.3% saved)

bsearch74.0ms (1.5%)

Steps

Iters	Range		Point
9	4.0797434017100284e-18	1.2754341939463802e-11	1.2601027867390625e-11
9	-0.02329983982683788	-1.342197564908979e-07	-1.3624134031553293e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	81
1	49	81

end0.0ms (0%)

sample3.1s (63.9%)

Algorithm

1×

intervals

Results

1.2s	3563×	body	1024	valid
623.0ms	1202×	body	2048	valid
280.0ms	1442×	body	512	valid
77.0ms	1257×	body	128	valid
66.0ms	535×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 634 to 507 computations (20% saved)

Details

analyze104.0ms (2.1%)

sample69.0ms (1.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite17.0ms (0.4%)

series51.0ms (1%)

simplify57.0ms (1.2%)

prune27.0ms (0.5%)

localize14.0ms (0.3%)

rewrite21.0ms (0.4%)

series83.0ms (1.7%)

simplify78.0ms (1.6%)

prune67.0ms (1.4%)

localize13.0ms (0.3%)

rewrite28.0ms (0.6%)

series141.0ms (2.9%)

simplify80.0ms (1.6%)

prune131.0ms (2.7%)

localize15.0ms (0.3%)

rewrite21.0ms (0.4%)

series236.0ms (4.8%)

simplify72.0ms (1.5%)

prune93.0ms (1.9%)

regimes265.0ms (5.4%)

bsearch74.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (63.9%)

Profiling