Details

analyze2.2s (21.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample52.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
9.0ms	116×	body	128	nan
4.0ms	52×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify202.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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: 13.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.2b	(/.f64 (.f64 M D) (.f64 2 d))
5.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
8.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
38×	`add-sqr-sqrt_binary64_1133`
27×	`prod-exp_binary64_1160`
23×	`add-cbrt-cube_binary64_1147`
19×	`associate-r_binary64_1051` `div-exp_binary64_1162`
17×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
15×	`times-frac_binary64_1117`
13×	`associate-l_binary64_1052`
10×	`pow-exp_binary64_1179` `unswap-sqr_binary64_1079`
7×	`unpow-prod-down_binary64_1190` `cbrt-unprod_binary64_1144` `pow1_binary64_1172` `sqrt-prod_binary64_1127`
5×	`cbrt-undiv_binary64_1145`
4×	`sqrt-div_binary64_1128` `add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `unpow2_binary64_1176` `sqr-pow_binary64_1083` `associate-*r/_binary64_1053`
2×	`*-commutative_binary64_1042` `flip3--_binary64_1115` `pow-to-exp_binary64_1180` `flip--_binary64_1086`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110`

Counts

4 → 116

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.0s (9.8%)

Counts

4 → 12

Calls

4 calls:

501.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
308.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
154.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5599	2845

prune367.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 7.0b

Counts

129 → 9

Compiler

Compiled 6912 to 4938 computations (28.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.1b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
26×	`prod-exp_binary64_1160`
23×	`add-cbrt-cube_binary64_1147`
20×	`add-sqr-sqrt_binary64_1133` `div-exp_binary64_1162`
13×	`*-un-lft-identity_binary64_1111`
10×	`add-cube-cbrt_binary64_1146` `associate-r_binary64_1051` `pow-exp_binary64_1179`
6×	`unpow-prod-down_binary64_1190` `cbrt-unprod_binary64_1144` `cbrt-undiv_binary64_1145` `sqrt-prod_binary64_1127`
5×	`times-frac_binary64_1117` `pow1_binary64_1172`
4×	`associate-/r*_binary64_1055` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `associate-l_binary64_1052`
2×	`sqrt-div_binary64_1128` `unpow2_binary64_1176` `frac-2neg_binary64_1122` `associate-/l*_binary64_1056` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180` `clear-num_binary64_1110`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `flip3--_binary64_1115` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`

Counts

4 → 99

Calls

4 calls:

9.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series980.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

568.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
192.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
178.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5310	2178

prune208.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Merged error: 7.0b

Counts

120 → 8

Compiler

Compiled 3839 to 2746 computations (28.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(*.f64 (/.f64 M 2) (/.f64 D d))
4.2b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
5.1b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
5.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1149`
43×	`add-sqr-sqrt_binary64_1133`
26×	`prod-exp_binary64_1160` `*-un-lft-identity_binary64_1111`
25×	`times-frac_binary64_1117`
23×	`add-cbrt-cube_binary64_1147` `add-cube-cbrt_binary64_1146`
20×	`div-exp_binary64_1162`
19×	`associate-r_binary64_1051`
16×	`associate-l_binary64_1052`
10×	`pow-exp_binary64_1179`
7×	`unswap-sqr_binary64_1079` `pow1_binary64_1172`
6×	`cbrt-unprod_binary64_1144` `cbrt-undiv_binary64_1145` `sqrt-prod_binary64_1127`
4×	`add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `associate-/r*_binary64_1055`
2×	`*-commutative_binary64_1042` `sqrt-div_binary64_1128` `unpow2_binary64_1176` `difference-of-squares_binary64_1080` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180`
1×	`pow1/2_binary64_1191` `unpow-prod-down_binary64_1190` `associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `frac-times_binary64_1121` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `associate-/l_binary64_1056` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086` `associate-*r/_binary64_1053`

Counts

4 → 123

Calls

4 calls:

13.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
8.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
7.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
7.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

series952.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

578.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
177.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
158.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
39.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5360	2553

prune191.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 7.0b

Counts

143 → 9

Compiler

Compiled 3809 to 2488 computations (34.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h)))
4.0b	(*.f64 (/.f64 M 2) (/.f64 D d))
5.1b	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)
5.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

170×	`add-exp-log_binary64_1149`
96×	`prod-exp_binary64_1160`
37×	`add-sqr-sqrt_binary64_1133` `div-exp_binary64_1162`
34×	`add-cbrt-cube_binary64_1147`
25×	`times-frac_binary64_1117`
24×	`*-un-lft-identity_binary64_1111`
21×	`add-cube-cbrt_binary64_1146`
20×	`cbrt-unprod_binary64_1144` `pow-exp_binary64_1179`
14×	`associate-r_binary64_1051` `associate-l_binary64_1052`
12×	`pow1_binary64_1172`
9×	`cbrt-undiv_binary64_1145`
6×	`sqrt-prod_binary64_1127`
4×	`pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150` `pow-to-exp_binary64_1180`
3×	`div-inv_binary64_1108` `associate-/r*_binary64_1055`
2×	`*-commutative_binary64_1042` `sqrt-div_binary64_1128` `difference-of-squares_binary64_1080`
1×	`pow1/2_binary64_1191` `associate-l/_binary64_1054` `rem-sqrt-square_binary64_1124` `frac-times_binary64_1121` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `associate-/l_binary64_1056` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086` `associate-*r/_binary64_1053`

Counts

4 → 139

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)
14.0ms	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h)))
13.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
9.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)))

series1.2s (11.8%)

Counts

4 → 12

Calls

4 calls:

713.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)))
253.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h))) l)
208.0ms	(.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2) (cbrt.f64 h)))
40.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	2920

prune191.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Merged error: 7.0b

Counts

160 → 9

Compiler

Compiled 3929 to 2208 computations (43.8% saved)

regimes416.0ms (4.1%)

Compiler: Compiled 3041 to 2813 computations (7.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 10 computations (-42.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	94
1	133	94

end0.0ms (0%)

sample1.7s (16.6%)

Algorithm

1×

intervals

Results

618.0ms	8000×	body	128	valid
256.0ms	3115×	body	128	nan
106.0ms	1300×	body	128	invalid

Compiler

Compiled 288 to 250 computations (13.2% saved)

Details

analyze2.2s (21.8%)

sample52.0ms (0.5%)

simplify202.0ms (2%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite50.0ms (0.5%)

series1.0s (9.8%)

simplify59.0ms (0.6%)

prune367.0ms (3.6%)

localize14.0ms (0.1%)

rewrite41.0ms (0.4%)

series980.0ms (9.5%)

simplify64.0ms (0.6%)

prune208.0ms (2%)

localize15.0ms (0.1%)

rewrite48.0ms (0.5%)

series952.0ms (9.3%)

simplify55.0ms (0.5%)

prune191.0ms (1.9%)

localize19.0ms (0.2%)

rewrite73.0ms (0.7%)

series1.2s (11.8%)

simplify83.0ms (0.8%)

prune191.0ms (1.9%)

regimes416.0ms (4.1%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (16.6%)

Profiling